This document provides 65 examples of tutorials that construct function tables and graphs for tangent functions of the form y = tan(ax + b) + c. Each tutorial varies the values of a, b, and c to illustrate different characteristics of tangent graphs.
Tutorials--Sine Functions in Tabular and Graph Form Media4math
This document describes 65 tutorials that provide examples of constructing tables and graphs for sine functions of the form y = a*sin(bx + c) + d, with varying values for the coefficients a, b, c, and d. Each tutorial works through an example with different coefficient values to demonstrate how to represent sine functions in tabular and graphical form for different periodic behaviors and vertical and horizontal shifts.
Tutorials--Cosecant Functions in Tabular and Graph FormMedia4math
This document describes 65 tutorials that provide examples of constructing tables and graphs for cosecant functions. Each tutorial examines a cosecant function of the form y = csc(ax + b) or y = a * csc(bx + c) + d with different values for the variables a, b, c, and d. The tutorials demonstrate how changing the values of these variables affects the shape of the cosecant function graph and its table of values.
Tutorials--Secant Functions in Tabular and Graph Form Media4math
This document describes 65 tutorials that provide examples of constructing tables and graphs for secant functions of the form y = sec(ax + b) + c, where a, b, and c can have various values. Each tutorial examines a different combination of values for a, b, and c to demonstrate secant functions with different periodic behaviors and shifts.
Tutorials--Square Root Functions in Tabular and Graph Form Media4math
This document provides 40 examples of tutorials for constructing tables and graphs of square root functions. Each tutorial examines a square root function of the form y = sqrt(ax + b) + c or y = d * sqrt(ax + b) + c, varying the values of a, b, c, and d to demonstrate different forms of square root functions.
Tutorials--Cosine Functions in Tabular and Graph Form Media4math
This document describes 65 tutorials on constructing tables and graphs for cosine functions of the form y=cos(ax+b). Each tutorial varies the values of a and b to demonstrate different characteristics of the cosine function graphed and tabulated over changing domains. The tutorials cover different positive, negative, and fractional values of a and various phase shifts introduced by changing the value of b.
Tutorials--Logarithmic Functions in Tabular and Graph Form Media4math
This document contains 120 examples of tutorials that construct function tables and graphs for logarithmic functions in tabular and graph form. The tutorials vary the base of the logarithm (base 10 or base 2), the characteristics of the logarithmic function (values of a, b, c for the function y = log(ax + b) + c), and whether the function has a single logarithm or a scaled logarithm (with coefficient d).
Tutorials--Absolute Value Functions in Tabular and Graph Form Media4math
This document provides 40 examples of tutorials for constructing tables and graphs of absolute value functions. Each tutorial examines a different form of the absolute value function y = |ax + b| + c with varying values for the coefficients a, b, c, and d. The tutorials explore all possible combinations of coefficient values.
Tutorials--Cube Root Functions in Tabular and Graph Form Media4math
This document provides 40 examples of tutorials that construct function tables and graphs for cube root functions of the form y=cuberoot(ax+b)+c. Each tutorial varies the values of a, b, and c to illustrate different forms of cube root functions.
Tutorials--Quadratic Functions in Tabular and Graphic FormMedia4math
This document provides 37 examples of tutorials that construct function tables and graphs for quadratic functions in standard form with varying characteristics for the coefficients a, b, and c. Each tutorial example uses a different combination of positive, negative, and zero values for the coefficients to illustrate different forms of quadratic functions.
Tutorials--Exponential Functions in Tabular and Graph FormMedia4math
This document outlines 54 tutorials that provide examples of constructing tables and graphs for exponential functions of various bases (2, 10, e) and characteristics of the coefficients a and b. Each tutorial works through an example of an exponential function of the form y = a*b^x, varying the values of a and b to illustrate different patterns in the table and graph.
The document discusses different forms and methods for graphing linear functions, including:
1) The standard, point-slope, and slope-intercept forms of linear equations.
2) Converting between these forms by solving for slope and y-intercept.
3) Graphing linear functions by finding the slope from two points using the point-slope form, making a table of x-y values, or finding the x- and y-intercepts.
4) Determining if two functions are parallel or perpendicular based on having equal or reciprocal slopes.
Tutorials: Graphs of Quadratic Functions in Standard FormMedia4math
This document outlines 18 examples of graphs of quadratic functions in standard form. The examples systematically vary the parameters a, b, and c to demonstrate how changing these parameters affects the shape and position of the graph of the quadratic function. Specifically, it explores how the graph is impacted when a, b, and c are positive versus negative values, as well as when they are equal to zero.
This document summarizes a lecture on raster graphics and rasterization. It discusses:
1) The 2D graphics pipeline which converts object coordinates to screen coordinates through transformations and rasterization.
2) Rasterization which converts geometry like lines, circles and triangles to pixel colors in the frame buffer by determining which pixels are turned on.
3) Line drawing algorithms like the digital differential analyzer (DDA) and Bresenham's algorithm which determine the pixels that lie on a line between two end points using slope and rounding.
4) How Bresenham's algorithm works by comparing the line equation to a midpoint to determine whether the y-value should increase or stay the same when incrementing x.
This PowerPoint was created to help out graduating seniors who are taking the TAKS Mathematics Exit-Level test. It includes formulas, rules & things that they need to remember to pass the test.
This document discusses the key elements of a quadratic function f(x) = ax^2 + bx + c. It explains that:
1) The y-intercept is indicated by the c coefficient as (0,c)
2) The vertex is calculated as (-b/2a, f(-b/2a))
3) The axis of symmetry passes through the vertex and is the line x=-b/2a.
It provides an example of the quadratic function f(x)=x^2+2x-8 and graphs it to illustrate these elements.
Tutorials--Rational Functions in Tabular and Graph FormMedia4math
This document provides 28 tutorials that construct function tables and graphs for rational functions of the form f(x) = a/(bx + c) + d, where a, b, c, and d are varied constants. Each tutorial works through an example of representing a rational function in both tabular and graphical form.
SAMPLE QUESTIONExercise 1 Consider the functionf (x,C).docxagnesdcarey33086
SAMPLE QUESTION:
Exercise 1: Consider the function
f (x,C)=
sin(C x)
Cx
(a) Create a vector x with 100 elements from -3*pi to 3*pi. Write f as an inline or anonymous function
and generate the vectors y1 = f(x,C1), y2 = f(x,C2) and y3 = f(x,C3), where C1 = 1, C2 = 2 and
C3 = 3. Make sure you suppress the output of x and y's vectors. Plot the function f (for the three
C's above), name the axis, give a title to the plot and include a legend to identify the plots. Add a
grid to the plot.
(b) Without using inline or anonymous functions write a function+function structure m-file that does
the same job as in part (a)
SAMPLE LAB WRITEUP:
MAT 275 MATLAB LAB 1 NAME: __________________________
LAB DAY and TIME:______________
Instructor: _______________________
Exercise 1
(a)
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
f= @(x,C) sin(C*x)./(C*x) % C will be just a constant, no need for ".*"
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % supressing the y's
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
Command window output:
f =
@(x,C)sin(C*x)./(C*x)
C1 =
1
C2 =
2
C3 =
3
(b)
M-file of structure function+function
function ex1
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % function f is defined below
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
end
function y = f(x,C)
y = sin(C*x)./(C*x);
end
Command window output:
C1 =
1
C2 =
2
C3 =
3
Joe Bob
Mon lab: 4:30-6:50
Lab 3
Exercise 1
(a) Create function M-file for banded LU factorization
function [L,U] = luband(A,p)
% LUBAND Banded LU factorization
% Adaptation to LUFACT
% Input:
% A diagonally dominant square matrix
% Output:
% L,U unit lower triangular and upper triangular such that LU=A
n = length(A);
L = eye(n); % ones on diagonal
% Gaussian Elimination
for j = 1:n-1
a = min(j+p.
This document provides 32 examples of solving one-step equations involving addition, subtraction, multiplication, and division. The examples cover equations with integer and decimal values where the unknown variable x is being solved for. Each example works through solving a different type of one-step equation, with the full set of examples addressing equations of the basic forms x ± a = b, a × x = b, and x ÷ a = b.
Lab 5 template Lab 5 - Your Name - MAT 275 Lab The M.docxsmile790243
Lab 5 template
%% Lab 5 - Your Name - MAT 275 Lab
% The Mass-Spring System
%% EX 1 10 pts
%A) 1 pts | short comment
%
%B) 2 pts | short comment
%
%C) 1 pts | short comment
%
%D) 1 pts
%E) 2 pts | List the first 3-4 t values either in decimal format or as
%fractions involving pi
%F) 3 pts | comments. | (1 pts for including two distinct graphs, each with y(t) and v(t) plotted)
%% EX 2 10 pts
%A) 5 pts
% add commands to LAB05ex1 to compute and plot E(t). Then use ylim([~,~]) to change the yaxis limits.
% You don't need to include this code but at least one plot of E(t) and a comment must be
% included!
%B) 2 pts | write out main steps here
% first differentiate E(t) with respect to t using the chain rule. Then
% make substitutions using the expression for omega0 and using the
% differential equation
%C) 3 pts | show plot and comment
%% EX 3 10 pts
%A) 3 pts | modify the system of equations in LAB05ex1a
% write the t value and either a) show correponding graph or b) explain given matlab
% commands
%B) 2 pts | write t value and max |V| value; include figure
%note: velocity magnitude is like absolute value!
%C) 3 pts | include 3 figures here + comments.
% use title('text') to attach a title to the figure
%D) 2 pts | What needs to happen (in terms of the characteristic equation)
%in order for there to be no oscillations? Impose a condition on the
%characteristic equation to find the critical c value. Write out main steps
%% EX4 10 pts
% A) 5 pts | include 1 figure and comment
%B) 2 pts
% again find dE/dt using the chain rule and make substitutions based on the
% differential equation. You should reach an expression for dE/dt which is
% in terms of y'
%C) 3 pts | include one figure and comment
Exercise (1):
function LAB05ex1
m = 1; % mass [kg]
k = 9; % spring constant [N/m]
omega0=sqrt(k/m);
y0=0.4; v0=0; % initial conditions
[t,Y]=ode45(@f,[0,10],[y0,v0],[],omega0); % solve for 0<t<10
y=Y(:,1); v=Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,'b+-',t,v,'ro-'); % time series for y and v
grid on;
%------------------------------------------------------
function dYdt= f(t,Y,omega0)
y = Y(1); v= Y(2);
dYdt = [v; -omega0^2*y];
Exercise (1a):
function LAB05ex1a
m = 1; % mass [kg]
k = 9; % spring constant [N/m]
c = 1; % friction coefficient [Ns/m]
omega0 = sqrt(k/m); p = c/(2*m);
y0 = 0.4; v0 = 0; % initial conditions
[t,Y]=ode45(@f,[0,10],[y0,v0],[],omega0,p); % solve for 0<t<10
y=Y(:,1); v=Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,'b+-',t,v,'ro-'); % time series for y and v
grid on
%------------------------------------------------------
function dYdt= f(t,Y,omega0,p)
y = Y(1); v= Y(2);
dYdt = [v; ?? ]; % fill-in dv/dt
More instructions for the l ...
This document provides instructions on how to evaluate algebraic expressions using a Casio fx-350ES PLUS calculator. It includes an example of evaluating the expression a2+b3 when a=4 and b=2. The steps shown are to assign the values 4 and 2 to the variables a and b using the calculator's storage function, then using the variables to calculate the expression. Exercises are provided to evaluate other algebraic expressions using the given calculator.
This document provides instructions on how to evaluate algebraic expressions using a Casio fx-350ES PLUS calculator. It includes an example of evaluating the expression a2+b3 when a=4 and b=2. The steps shown are to assign the values 4 and 2 to the variables a and b using the calculator's storage function, then using the variables to calculate the expression. Exercises are provided to evaluate other algebraic expressions using the given calculator.
This document discusses functions and how they can be represented in three ways: as a function rule, as a table of ordered pairs, and as a graph. It provides examples of modeling functions using each representation. It also discusses using functions to model real-world situations like the costs of producing CDs for different numbers of copies. Functions can have linear graphs or non-linear graphs like parabolas or absolute value graphs. Learners are asked to complete tables, graph functions, compare costs at different quantities, and graph additional functions.
The document discusses different types of modeling involving functions. It provides examples of exponential, logarithmic, and circular functions where the variables or constants are missing and points on the graphs are given. Readers are instructed to find the values of the missing variables or constants by inserting the points into the corresponding function equations. Exercises from the textbook are assigned for practice.
MATLAB sessions: Laboratory 2
MAT 275 Laboratory 2
Matrix Computations and Programming in MATLAB
In this laboratory session we will learn how to
1. Create and manipulate matrices and vectors.
2. Write simple programs in MATLAB
NOTE: For your lab write-up, follow the instructions of LAB1.
Matrices and Linear Algebra
⋆ Matrices can be constructed in MATLAB in different ways. For example the 3 × 3 matrix
A =
8 1 63 5 7
4 9 2
can be entered as
>> A=[8,1,6;3,5,7;4,9,2]
A =
8 1 6
3 5 7
4 9 2
or
>> A=[8,1,6;
3,5,7;
4,9,2]
A =
8 1 6
3 5 7
4 9 2
or defined as the concatenation of 3 rows
>> row1=[8,1,6]; row2=[3,5,7]; row3=[4,9,2]; A=[row1;row2;row3]
A =
8 1 6
3 5 7
4 9 2
or 3 columns
>> col1=[8;3;4]; col2=[1;5;9]; col3=[6;7;2]; A=[col1,col2,col3]
A =
8 1 6
3 5 7
4 9 2
Note the use of , and ;. Concatenated rows/columns must have the same length. Larger matrices can
be created from smaller ones in the same way:
c⃝2011 Stefania Tracogna, SoMSS, ASU
MATLAB sessions: Laboratory 2
>> C=[A,A] % Same as C=[A A]
C =
8 1 6 8 1 6
3 5 7 3 5 7
4 9 2 4 9 2
The matrix C has dimension 3 × 6 (“3 by 6”). On the other hand smaller matrices (submatrices) can
be extracted from any given matrix:
>> A(2,3) % coefficient of A in 2nd row, 3rd column
ans =
7
>> A(1,:) % 1st row of A
ans =
8 1 6
>> A(:,3) % 3rd column of A
ans =
6
7
2
>> A([1,3],[2,3]) % keep coefficients in rows 1 & 3 and columns 2 & 3
ans =
1 6
9 2
⋆ Some matrices are already predefined in MATLAB:
>> I=eye(3) % the Identity matrix
I =
1 0 0
0 1 0
0 0 1
>> magic(3)
ans =
8 1 6
3 5 7
4 9 2
(what is magic about this matrix?)
⋆ Matrices can be manipulated very easily in MATLAB (unlike Maple). Here are sample commands
to exercise with:
>> A=magic(3);
>> B=A’ % transpose of A, i.e, rows of B are columns of A
B =
8 3 4
1 5 9
6 7 2
>> A+B % sum of A and B
ans =
16 4 10
4 10 16
10 16 4
>> A*B % standard linear algebra matrix multiplication
ans =
101 71 53
c⃝2011 Stefania Tracogna, SoMSS, ASU
MATLAB sessions: Laboratory 2
71 83 71
53 71 101
>> A.*B % coefficient-wise multiplication
ans =
64 3 24
3 25 63
24 63 4
⋆ One MATLAB command is especially relevant when studying the solution of linear systems of dif-
ferentials equations: x=A\b determines the solution x = A−1b of the linear system Ax = b. Here is an
example:
>> A=magic(3);
>> z=[1,2,3]’ % same as z=[1;2;3]
z =
1
2
3
>> b=A*z
b =
28
34
28
>> x = A\b % solve the system Ax = b. Compare with the exact solution, z, defined above.
x =
1
2
3
>> y =inv(A)*b % solve the system using the inverse: less efficient and accurate
ans =
1.0000
2.0000
3.0000
Now let’s check for accuracy by evaluating the difference z − x and z − y. In exact arithmetic they
should both be zero since x, y and z all represent the solution to the system.
>> z - x % error for backslash command
ans =
0
0
0
>> z - y % error for inverse
ans =
1.0e-015 *
-0.4441
0
-0.88 ...
1. The document discusses types of transformations of graphs of functions, including translations, scale changes, and reflections. It uses the example of the path of a basketball shot into the air to illustrate these transformations.
2. The basketball shooting example provides data that is used to determine the parabolic function that models the ball's height over time. This function is then transformed through various translations, scale changes, and reflections using GeoGebra to analyze the effects on the graph.
3. Key effects of the transformations include changing the graph's position (translations), stretching or shrinking along the axes (scale changes), and flipping the graph across an axis (reflections when the scale factor is -1). The domain and range may
Here are the key steps to solve this problem algebraically:
Let x = number of units of product X
Let y = number of units of product Y
Write equations relating the process hours to the number of units:
3x + 2x = Hours used in A
1y + 4y = Hours used in B
Solve the simultaneous equations to find the maximum number of each product that can be made.
More instructions for the lab write-up1) You are not obli.docxgilpinleeanna
More instructions for the lab write-up:
1) You are not obligated to use the 'diary' function. It was presented only for you convenience. You
should be copying and pasting your code, plots, and results into some sort of "Word" type editor that
will allow you to import graphs and such. Make sure you always include the commands to generate
what is been asked and include the outputs (from command window and plots), unless the problem
says to suppress it.
2) Edit this document: there should be no code or MATLAB commands that do not pertain to the
exercises you are presenting in your final submission. For each exercise, only the relevant code that
performs the task should be included. Do not include error messages. So once you have determined
either the command line instructions or the appropriate script file that will perform the task you are
given for the exercise, you should only include that and the associated output. Copy/paste these into
your final submission document followed by the output (including plots) that these MATLAB
instructions generate.
3) All code, output and plots for an exercise are to be grouped together. Do not put them in appendix, at
the end of the writeup, etc. In particular, put any mfiles you write BEFORE you first call them.
Each exercise, as well as the part of the exercises, is to be clearly demarked. Do not blend them all
together into some sort of composition style paper, complimentary to this: do NOT double space.
You can have spacing that makes your lab report look nice, but do not double space sections of text
as you would in a literature paper.
4) You can suppress much of the MATLAB output. If you need to create a vector, "x = 0:0.1:10" for
example, for use, there is no need to include this as output in your writeup. Just make sure you
include whatever result you are asked to show. Plots also do not have to be a full, or even half page.
They just have to be large enough that the relevant structure can be seen.
5) Before you put down any code, plots, etc. answer whatever questions that the exercise asks first.
You will follow this with the results of your work that support your answer.
SAMPLE QUESTION:
Exercise 1: Consider the function
f (x,C)=
sin(C x)
Cx
(a) Create a vector x with 100 elements from -3*pi to 3*pi. Write f as an inline or anonymous function
and generate the vectors y1 = f(x,C1), y2 = f(x,C2) and y3 = f(x,C3), where C1 = 1, C2 = 2 and
C3 = 3. Make sure you suppress the output of x and y's vectors. Plot the function f (for the three
C's above), name the axis, give a title to the plot and include a legend to identify the plots. Add a
grid to the plot.
(b) Without using inline or anonymous functions write a function+function structure m-file that does
the same job as in part (a)
SAMPLE LAB WRITEUP:
MAT 275 MATLAB LAB 1 NAME: ...
Here are the key steps to solve this problem algebraically:
Let x = number of units of product X
Let y = number of units of product Y
Equation for process A: 3x + y ≤ 1750
Equation for process B: 2x + 4y ≤ 4000
Solve the two equations simultaneously using elimination:
3x + y = 1750
2x + 4y = 4000
Eliminate y by subtracting the equations:
x = 1250
Substitute x = 1250 into one of the original equations to find y:
3(1250) + y = 1750
y = 500
Therefore, the maximum number of units of X is 1250 and
This document discusses algorithms and data structures. It begins by defining an algorithm as a set of instructions to accomplish a task and lists criteria such as being unambiguous and terminating. Data types and abstract data types are introduced. Methods for analyzing programs are covered, including time and space complexity using asymptotic notation. Examples are provided to illustrate iterative and recursive algorithms for summing lists as well as matrix operations.
Tutorials--Quadratic Functions in Tabular and Graphic FormMedia4math
This document provides 37 examples of tutorials that construct function tables and graphs for quadratic functions in standard form with varying characteristics for the coefficients a, b, and c. Each tutorial example uses a different combination of positive, negative, and zero values for the coefficients to illustrate different forms of quadratic functions.
Tutorials--Exponential Functions in Tabular and Graph FormMedia4math
This document outlines 54 tutorials that provide examples of constructing tables and graphs for exponential functions of various bases (2, 10, e) and characteristics of the coefficients a and b. Each tutorial works through an example of an exponential function of the form y = a*b^x, varying the values of a and b to illustrate different patterns in the table and graph.
The document discusses different forms and methods for graphing linear functions, including:
1) The standard, point-slope, and slope-intercept forms of linear equations.
2) Converting between these forms by solving for slope and y-intercept.
3) Graphing linear functions by finding the slope from two points using the point-slope form, making a table of x-y values, or finding the x- and y-intercepts.
4) Determining if two functions are parallel or perpendicular based on having equal or reciprocal slopes.
Tutorials: Graphs of Quadratic Functions in Standard FormMedia4math
This document outlines 18 examples of graphs of quadratic functions in standard form. The examples systematically vary the parameters a, b, and c to demonstrate how changing these parameters affects the shape and position of the graph of the quadratic function. Specifically, it explores how the graph is impacted when a, b, and c are positive versus negative values, as well as when they are equal to zero.
This document summarizes a lecture on raster graphics and rasterization. It discusses:
1) The 2D graphics pipeline which converts object coordinates to screen coordinates through transformations and rasterization.
2) Rasterization which converts geometry like lines, circles and triangles to pixel colors in the frame buffer by determining which pixels are turned on.
3) Line drawing algorithms like the digital differential analyzer (DDA) and Bresenham's algorithm which determine the pixels that lie on a line between two end points using slope and rounding.
4) How Bresenham's algorithm works by comparing the line equation to a midpoint to determine whether the y-value should increase or stay the same when incrementing x.
This PowerPoint was created to help out graduating seniors who are taking the TAKS Mathematics Exit-Level test. It includes formulas, rules & things that they need to remember to pass the test.
This document discusses the key elements of a quadratic function f(x) = ax^2 + bx + c. It explains that:
1) The y-intercept is indicated by the c coefficient as (0,c)
2) The vertex is calculated as (-b/2a, f(-b/2a))
3) The axis of symmetry passes through the vertex and is the line x=-b/2a.
It provides an example of the quadratic function f(x)=x^2+2x-8 and graphs it to illustrate these elements.
Tutorials--Rational Functions in Tabular and Graph FormMedia4math
This document provides 28 tutorials that construct function tables and graphs for rational functions of the form f(x) = a/(bx + c) + d, where a, b, c, and d are varied constants. Each tutorial works through an example of representing a rational function in both tabular and graphical form.
SAMPLE QUESTIONExercise 1 Consider the functionf (x,C).docxagnesdcarey33086
SAMPLE QUESTION:
Exercise 1: Consider the function
f (x,C)=
sin(C x)
Cx
(a) Create a vector x with 100 elements from -3*pi to 3*pi. Write f as an inline or anonymous function
and generate the vectors y1 = f(x,C1), y2 = f(x,C2) and y3 = f(x,C3), where C1 = 1, C2 = 2 and
C3 = 3. Make sure you suppress the output of x and y's vectors. Plot the function f (for the three
C's above), name the axis, give a title to the plot and include a legend to identify the plots. Add a
grid to the plot.
(b) Without using inline or anonymous functions write a function+function structure m-file that does
the same job as in part (a)
SAMPLE LAB WRITEUP:
MAT 275 MATLAB LAB 1 NAME: __________________________
LAB DAY and TIME:______________
Instructor: _______________________
Exercise 1
(a)
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
f= @(x,C) sin(C*x)./(C*x) % C will be just a constant, no need for ".*"
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % supressing the y's
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
Command window output:
f =
@(x,C)sin(C*x)./(C*x)
C1 =
1
C2 =
2
C3 =
3
(b)
M-file of structure function+function
function ex1
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % function f is defined below
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
end
function y = f(x,C)
y = sin(C*x)./(C*x);
end
Command window output:
C1 =
1
C2 =
2
C3 =
3
Joe Bob
Mon lab: 4:30-6:50
Lab 3
Exercise 1
(a) Create function M-file for banded LU factorization
function [L,U] = luband(A,p)
% LUBAND Banded LU factorization
% Adaptation to LUFACT
% Input:
% A diagonally dominant square matrix
% Output:
% L,U unit lower triangular and upper triangular such that LU=A
n = length(A);
L = eye(n); % ones on diagonal
% Gaussian Elimination
for j = 1:n-1
a = min(j+p.
This document provides 32 examples of solving one-step equations involving addition, subtraction, multiplication, and division. The examples cover equations with integer and decimal values where the unknown variable x is being solved for. Each example works through solving a different type of one-step equation, with the full set of examples addressing equations of the basic forms x ± a = b, a × x = b, and x ÷ a = b.
Lab 5 template Lab 5 - Your Name - MAT 275 Lab The M.docxsmile790243
Lab 5 template
%% Lab 5 - Your Name - MAT 275 Lab
% The Mass-Spring System
%% EX 1 10 pts
%A) 1 pts | short comment
%
%B) 2 pts | short comment
%
%C) 1 pts | short comment
%
%D) 1 pts
%E) 2 pts | List the first 3-4 t values either in decimal format or as
%fractions involving pi
%F) 3 pts | comments. | (1 pts for including two distinct graphs, each with y(t) and v(t) plotted)
%% EX 2 10 pts
%A) 5 pts
% add commands to LAB05ex1 to compute and plot E(t). Then use ylim([~,~]) to change the yaxis limits.
% You don't need to include this code but at least one plot of E(t) and a comment must be
% included!
%B) 2 pts | write out main steps here
% first differentiate E(t) with respect to t using the chain rule. Then
% make substitutions using the expression for omega0 and using the
% differential equation
%C) 3 pts | show plot and comment
%% EX 3 10 pts
%A) 3 pts | modify the system of equations in LAB05ex1a
% write the t value and either a) show correponding graph or b) explain given matlab
% commands
%B) 2 pts | write t value and max |V| value; include figure
%note: velocity magnitude is like absolute value!
%C) 3 pts | include 3 figures here + comments.
% use title('text') to attach a title to the figure
%D) 2 pts | What needs to happen (in terms of the characteristic equation)
%in order for there to be no oscillations? Impose a condition on the
%characteristic equation to find the critical c value. Write out main steps
%% EX4 10 pts
% A) 5 pts | include 1 figure and comment
%B) 2 pts
% again find dE/dt using the chain rule and make substitutions based on the
% differential equation. You should reach an expression for dE/dt which is
% in terms of y'
%C) 3 pts | include one figure and comment
Exercise (1):
function LAB05ex1
m = 1; % mass [kg]
k = 9; % spring constant [N/m]
omega0=sqrt(k/m);
y0=0.4; v0=0; % initial conditions
[t,Y]=ode45(@f,[0,10],[y0,v0],[],omega0); % solve for 0<t<10
y=Y(:,1); v=Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,'b+-',t,v,'ro-'); % time series for y and v
grid on;
%------------------------------------------------------
function dYdt= f(t,Y,omega0)
y = Y(1); v= Y(2);
dYdt = [v; -omega0^2*y];
Exercise (1a):
function LAB05ex1a
m = 1; % mass [kg]
k = 9; % spring constant [N/m]
c = 1; % friction coefficient [Ns/m]
omega0 = sqrt(k/m); p = c/(2*m);
y0 = 0.4; v0 = 0; % initial conditions
[t,Y]=ode45(@f,[0,10],[y0,v0],[],omega0,p); % solve for 0<t<10
y=Y(:,1); v=Y(:,2); % retrieve y, v from Y
figure(1); plot(t,y,'b+-',t,v,'ro-'); % time series for y and v
grid on
%------------------------------------------------------
function dYdt= f(t,Y,omega0,p)
y = Y(1); v= Y(2);
dYdt = [v; ?? ]; % fill-in dv/dt
More instructions for the l ...
This document provides instructions on how to evaluate algebraic expressions using a Casio fx-350ES PLUS calculator. It includes an example of evaluating the expression a2+b3 when a=4 and b=2. The steps shown are to assign the values 4 and 2 to the variables a and b using the calculator's storage function, then using the variables to calculate the expression. Exercises are provided to evaluate other algebraic expressions using the given calculator.
This document provides instructions on how to evaluate algebraic expressions using a Casio fx-350ES PLUS calculator. It includes an example of evaluating the expression a2+b3 when a=4 and b=2. The steps shown are to assign the values 4 and 2 to the variables a and b using the calculator's storage function, then using the variables to calculate the expression. Exercises are provided to evaluate other algebraic expressions using the given calculator.
This document discusses functions and how they can be represented in three ways: as a function rule, as a table of ordered pairs, and as a graph. It provides examples of modeling functions using each representation. It also discusses using functions to model real-world situations like the costs of producing CDs for different numbers of copies. Functions can have linear graphs or non-linear graphs like parabolas or absolute value graphs. Learners are asked to complete tables, graph functions, compare costs at different quantities, and graph additional functions.
The document discusses different types of modeling involving functions. It provides examples of exponential, logarithmic, and circular functions where the variables or constants are missing and points on the graphs are given. Readers are instructed to find the values of the missing variables or constants by inserting the points into the corresponding function equations. Exercises from the textbook are assigned for practice.
MATLAB sessions: Laboratory 2
MAT 275 Laboratory 2
Matrix Computations and Programming in MATLAB
In this laboratory session we will learn how to
1. Create and manipulate matrices and vectors.
2. Write simple programs in MATLAB
NOTE: For your lab write-up, follow the instructions of LAB1.
Matrices and Linear Algebra
⋆ Matrices can be constructed in MATLAB in different ways. For example the 3 × 3 matrix
A =
8 1 63 5 7
4 9 2
can be entered as
>> A=[8,1,6;3,5,7;4,9,2]
A =
8 1 6
3 5 7
4 9 2
or
>> A=[8,1,6;
3,5,7;
4,9,2]
A =
8 1 6
3 5 7
4 9 2
or defined as the concatenation of 3 rows
>> row1=[8,1,6]; row2=[3,5,7]; row3=[4,9,2]; A=[row1;row2;row3]
A =
8 1 6
3 5 7
4 9 2
or 3 columns
>> col1=[8;3;4]; col2=[1;5;9]; col3=[6;7;2]; A=[col1,col2,col3]
A =
8 1 6
3 5 7
4 9 2
Note the use of , and ;. Concatenated rows/columns must have the same length. Larger matrices can
be created from smaller ones in the same way:
c⃝2011 Stefania Tracogna, SoMSS, ASU
MATLAB sessions: Laboratory 2
>> C=[A,A] % Same as C=[A A]
C =
8 1 6 8 1 6
3 5 7 3 5 7
4 9 2 4 9 2
The matrix C has dimension 3 × 6 (“3 by 6”). On the other hand smaller matrices (submatrices) can
be extracted from any given matrix:
>> A(2,3) % coefficient of A in 2nd row, 3rd column
ans =
7
>> A(1,:) % 1st row of A
ans =
8 1 6
>> A(:,3) % 3rd column of A
ans =
6
7
2
>> A([1,3],[2,3]) % keep coefficients in rows 1 & 3 and columns 2 & 3
ans =
1 6
9 2
⋆ Some matrices are already predefined in MATLAB:
>> I=eye(3) % the Identity matrix
I =
1 0 0
0 1 0
0 0 1
>> magic(3)
ans =
8 1 6
3 5 7
4 9 2
(what is magic about this matrix?)
⋆ Matrices can be manipulated very easily in MATLAB (unlike Maple). Here are sample commands
to exercise with:
>> A=magic(3);
>> B=A’ % transpose of A, i.e, rows of B are columns of A
B =
8 3 4
1 5 9
6 7 2
>> A+B % sum of A and B
ans =
16 4 10
4 10 16
10 16 4
>> A*B % standard linear algebra matrix multiplication
ans =
101 71 53
c⃝2011 Stefania Tracogna, SoMSS, ASU
MATLAB sessions: Laboratory 2
71 83 71
53 71 101
>> A.*B % coefficient-wise multiplication
ans =
64 3 24
3 25 63
24 63 4
⋆ One MATLAB command is especially relevant when studying the solution of linear systems of dif-
ferentials equations: x=A\b determines the solution x = A−1b of the linear system Ax = b. Here is an
example:
>> A=magic(3);
>> z=[1,2,3]’ % same as z=[1;2;3]
z =
1
2
3
>> b=A*z
b =
28
34
28
>> x = A\b % solve the system Ax = b. Compare with the exact solution, z, defined above.
x =
1
2
3
>> y =inv(A)*b % solve the system using the inverse: less efficient and accurate
ans =
1.0000
2.0000
3.0000
Now let’s check for accuracy by evaluating the difference z − x and z − y. In exact arithmetic they
should both be zero since x, y and z all represent the solution to the system.
>> z - x % error for backslash command
ans =
0
0
0
>> z - y % error for inverse
ans =
1.0e-015 *
-0.4441
0
-0.88 ...
1. The document discusses types of transformations of graphs of functions, including translations, scale changes, and reflections. It uses the example of the path of a basketball shot into the air to illustrate these transformations.
2. The basketball shooting example provides data that is used to determine the parabolic function that models the ball's height over time. This function is then transformed through various translations, scale changes, and reflections using GeoGebra to analyze the effects on the graph.
3. Key effects of the transformations include changing the graph's position (translations), stretching or shrinking along the axes (scale changes), and flipping the graph across an axis (reflections when the scale factor is -1). The domain and range may
Here are the key steps to solve this problem algebraically:
Let x = number of units of product X
Let y = number of units of product Y
Write equations relating the process hours to the number of units:
3x + 2x = Hours used in A
1y + 4y = Hours used in B
Solve the simultaneous equations to find the maximum number of each product that can be made.
More instructions for the lab write-up1) You are not obli.docxgilpinleeanna
More instructions for the lab write-up:
1) You are not obligated to use the 'diary' function. It was presented only for you convenience. You
should be copying and pasting your code, plots, and results into some sort of "Word" type editor that
will allow you to import graphs and such. Make sure you always include the commands to generate
what is been asked and include the outputs (from command window and plots), unless the problem
says to suppress it.
2) Edit this document: there should be no code or MATLAB commands that do not pertain to the
exercises you are presenting in your final submission. For each exercise, only the relevant code that
performs the task should be included. Do not include error messages. So once you have determined
either the command line instructions or the appropriate script file that will perform the task you are
given for the exercise, you should only include that and the associated output. Copy/paste these into
your final submission document followed by the output (including plots) that these MATLAB
instructions generate.
3) All code, output and plots for an exercise are to be grouped together. Do not put them in appendix, at
the end of the writeup, etc. In particular, put any mfiles you write BEFORE you first call them.
Each exercise, as well as the part of the exercises, is to be clearly demarked. Do not blend them all
together into some sort of composition style paper, complimentary to this: do NOT double space.
You can have spacing that makes your lab report look nice, but do not double space sections of text
as you would in a literature paper.
4) You can suppress much of the MATLAB output. If you need to create a vector, "x = 0:0.1:10" for
example, for use, there is no need to include this as output in your writeup. Just make sure you
include whatever result you are asked to show. Plots also do not have to be a full, or even half page.
They just have to be large enough that the relevant structure can be seen.
5) Before you put down any code, plots, etc. answer whatever questions that the exercise asks first.
You will follow this with the results of your work that support your answer.
SAMPLE QUESTION:
Exercise 1: Consider the function
f (x,C)=
sin(C x)
Cx
(a) Create a vector x with 100 elements from -3*pi to 3*pi. Write f as an inline or anonymous function
and generate the vectors y1 = f(x,C1), y2 = f(x,C2) and y3 = f(x,C3), where C1 = 1, C2 = 2 and
C3 = 3. Make sure you suppress the output of x and y's vectors. Plot the function f (for the three
C's above), name the axis, give a title to the plot and include a legend to identify the plots. Add a
grid to the plot.
(b) Without using inline or anonymous functions write a function+function structure m-file that does
the same job as in part (a)
SAMPLE LAB WRITEUP:
MAT 275 MATLAB LAB 1 NAME: ...
Here are the key steps to solve this problem algebraically:
Let x = number of units of product X
Let y = number of units of product Y
Equation for process A: 3x + y ≤ 1750
Equation for process B: 2x + 4y ≤ 4000
Solve the two equations simultaneously using elimination:
3x + y = 1750
2x + 4y = 4000
Eliminate y by subtracting the equations:
x = 1250
Substitute x = 1250 into one of the original equations to find y:
3(1250) + y = 1750
y = 500
Therefore, the maximum number of units of X is 1250 and
This document discusses algorithms and data structures. It begins by defining an algorithm as a set of instructions to accomplish a task and lists criteria such as being unambiguous and terminating. Data types and abstract data types are introduced. Methods for analyzing programs are covered, including time and space complexity using asymptotic notation. Examples are provided to illustrate iterative and recursive algorithms for summing lists as well as matrix operations.
This document provides an introduction to MATLAB through examples of basic operations and functions. It demonstrates how to perform numeric calculations with scalars and vectors, plot graphs, work with matrices, and solve linear systems of equations. The key concepts covered include loading and saving variables, arithmetic operations, matrix operations, plotting functions, and the MATLAB command history.
- The document discusses various matrix operations including transpose, addition, subtraction, scalar multiplication, matrix multiplication, matrix-vector products, and finding the inverse of a matrix.
- Key operations include transposing a matrix, adding and subtracting matrices of the same size, multiplying a matrix by a scalar, multiplying two matrices if they are compatible in size, and taking the inverse of a square matrix if it exists.
- Properties such as commutativity, associativity, and how they apply to different matrix operations are also covered.
1. The document discusses the distributive property in mathematics, which states that for all real numbers a, b, and c, a(b + c) = ab + ac and a(b - c) = ab - ac.
2. It also explains that the distributive property can be extended to division, as long as the denominators are not equal to zero. For example, (ab - ac)/a = b - c.
3. An example is provided to demonstrate using the distributive property to simplify expressions such as a(b + c) and (ab - ac)/a when a = 5, b = 2, and c = 3.
Geometric Construction: Creating a Teardrop ShapeMedia4math
Constructing a teardrop shape involves drawing three circles of different radii using a compass on graph paper. The teardrop shape is formed by the overlapping circular arcs from a radius 5 circle, another radius 5 circle, and a radius 3 circle. The overlapping arcs are highlighted and isolated by erasing the remaining circular areas to reveal the smooth teardrop curve created by the intersecting arcs.
A hands-on activity for explore a variety of math topics, including:
* Circumference and Diameter
* Linear functions and slope
* Ratios
* Data gathering and scatterplot
For more math resources, go to www.media4math.com.
Math in the News: Issue 111--Summer BlockbustersMedia4math
The document discusses summer blockbuster movies. Some key points:
- Summer is the peak movie season due to school being out and families looking for affordable entertainment options.
- Blockbusters are big-budget films released in the summer that draw huge audiences and make substantial profits. They typically feature recognizable stars, special effects, and family-friendly content.
- Examples of past summer blockbusters that fit this profile are provided.
- Data on the budget and earnings of Avatar, a highly successful blockbuster, show it had a budget of $425 million and grossed $760.5 million, resulting in a profit of $335.5 million.
This document advertises the digital math resources available through Media4Math, including over 11,000 resources that can be purchased individually or through a subscription. It provides information about the Marketplace, Open Educational Resource library, Worksheet library, and libraries of resources focused on teaching linear functions, quadratic functions, and other math topics through videos, games, and presentations.
Tutorials--The Language of Math--Variable Expressions--Multiplication and Sub...Media4math
This set of tutorials provides 32 examples of converting verbal expressions into variable expressions that involve multiplication and subtraction. Note: The download is a PPT file.
Tutorials--The Language of Math--Numerical Expressions--Multiplication Media4math
This set of tutorials provides 40 examples of converting verbal expressions into numerical expressions that involve multiplication. Note: The download is a PPT file.
Tutorials--The Language of Math--Numerical Expressions--Division Media4math
This set of tutorials provides 40 examples of converting verbal expressions into numerical expressions that involve division. Note: The download is a PPT file.
Tutorials--The Language of Math--Numerical Expressions--SubtractionMedia4math
This set of tutorials provides 40 examples of converting verbal expressions into numerical expressions that involve subtraction. Note: The download is a PPT file.
Tutorials--Language of Math--Numerical Expressions--AdditionMedia4math
This set of tutorials provides 40 examples of converting verbal expressions into numerical expressions that involve addition. The verbal expressions include these terms:
Plus
Increased by
In addition to
Added to
More than
This document discusses using mathematical models to represent the thawing of frozen turkeys. It introduces logarithmic functions as a model for thawing curves, as the temperature increases over time in a way similar to the inverse of an exponential cooling curve. The document provides guidelines from the USDA for safely thawing turkeys either in the refrigerator over several days or in a water container over several hours, and shows how to construct a logarithmic model to fit starting and ending temperature points for a turkey thawing in the refrigerator.
Tutorials: Linear Functions in Tabular and Graph FormMedia4math
This document provides 21 examples of linear functions presented as both tables and graphs. Each example shows a linear function in slope-intercept form with different characteristics for the slope and y-intercept, such as positive and negative slopes greater than, less than, and equal to 1, as well as zero slopes and various y-intercepts. The examples cover a range of linear functions demonstrated visually and numerically.
1. Jurassic World has become one of the highest grossing films worldwide and is ranked 7th on the global box office list.
2. Domestically, Jurassic World is ranked 5th on the North American box office top 10 list after only a few weeks.
3. The data shows domestic and international box office figures for the top 10 highest grossing films worldwide, with international sales making up a higher percentage for most films compared to domestic sales.
This document provides examples for solving two-step equations. It contains 32 examples that involve combinations of addition, subtraction, multiplication, and division, and show the steps to solve for the unknown using the inverse operations. The examples are divided into two sets - the first 16 have only positive numbers, while the remaining 16 can have positive or negative numbers.
This document outlines 26 tutorials that provide examples of finding the range of data sets containing various numbers of positive and negative integers. Each tutorial finds the range for a different data set size ranging from 8 to 20 numbers.
Management of head injury in children.pdfsachin7989
Management of Head Injury: A Clinical Overview
1. Initial Assessment and Stabilization:
The management of a head injury begins with a rapid and systematic assessment using the ABCDE approach:
A – Airway: Ensure the airway is patent; consider cervical spine protection.
B – Breathing: Assess respiratory effort and oxygenation; provide supplemental oxygen if needed.
C – Circulation: Monitor pulse, blood pressure, and capillary refill; manage shock if present.
D – Disability: Evaluate neurological status using the Glasgow Coma Scale (GCS); assess pupil size and reactivity.
E – Exposure: Fully expose the patient to assess for other injuries while preventing hypothermia.
2. Classification of Head Injury:
Head injuries are classified based on GCS score:
Mild: GCS 13–15
Moderate: GCS 9–12
Severe: GCS ≤8
3. Imaging and Diagnosis:
CT scan of the head is the imaging modality of choice, especially in moderate to severe injuries, or if red flag symptoms are present (e.g., vomiting, seizures, focal neurological signs, skull fracture).
Cervical spine imaging may also be necessary.
4. Acute Management:
Mild head injury: Observation, symptomatic treatment (e.g., analgesics), and instructions for return precautions.
Moderate to severe head injury:
Admit to hospital, ideally in an intensive care unit (ICU) if GCS ≤8.
Maintain cerebral perfusion pressure (CPP): control blood pressure and intracranial pressure (ICP).
Consider hyperosmolar therapy (e.g., mannitol or hypertonic saline) if signs of raised ICP.
Elevate head of the bed to 30 degrees.
Surgical intervention (e.g., evacuation of hematomas) may be required based on CT findings.
5. Monitoring and Supportive Care:
Continuous monitoring of GCS, pupils, vitals, and neurological signs.
ICP monitoring in patients with severe injury.
Prevent secondary brain injury by optimizing oxygenation, ventilation, and perfusion.
Seizure prophylaxis may be considered in select cases.
6. Rehabilitation and Long-Term Care:
Referral for neurorehabilitation for physical, cognitive, and emotional recovery.
Psychological support and education for patient and family.
Regular follow-up to monitor for late complications like post-traumatic epilepsy, cognitive deficits, or behavioral changes.
7. Prevention:
Education on safety measures (e.g., helmets, seat belts).
Public health strategies to reduce road traffic accidents, falls, and violence.
TechSoup Introduction to Generative AI and Copilot - 2025.05.22.pdfTechSoup
In this engaging and insightful two-part webinar series, where we will dive into the essentials of generative AI, address key AI concerns, and demonstrate how nonprofits can benefit from using Microsoft’s AI assistant, Copilot, to achieve their goals.
This event series to help nonprofits obtain Copilot skills is made possible by generous support from Microsoft.
Are you struggling with Industrial Engineering topics like operations research, production planning, simulation, or supply chain management? This comprehensive Industrial Engineering Assignment Help Guide is designed to assist students in understanding and solving complex academic problems with ease and confidence.
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The role and benefits of expert assignment help and one-on-one tutoring support
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How to Automate Activities Using Odoo 18 CRMCeline George
In Odoo 18, the CRM module's activity feature is designed to help users manage and track tasks related to customer interactions. These tasks could include phone calls, meetings, emails, or follow-ups, and are essential for progressing through sales and customer management processes.
How to create Record rules in odoo 18 - Odoo SlidesCeline George
Record rules allow us to restrict which records are displayed to users. Creating record rules in Odoo 18 is essential for managing data access and ensuring that users can only see or interact with records they are authorized to access.
Automated Actions (Automation) in the Odoo 18Celine George
In this slide, we’ll discuss the automated actions in the Odoo 18. Automated actions in Odoo 18 enable users to set predefined actions triggered automatically by specified conditions or events.
AI and international projects. Helsinki 20.5.25Matleena Laakso
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Flower Identification Class-10 by Kushal Lamichhane.pdfkushallamichhame
This includes the overall cultivation practices of rose prepared by:
Kushal Lamichhane
Instructor
Shree Gandhi Adarsha Secondary School
Kageshowri Manohara-09, Kathmandu, Nepal
2. Overview
This set of tutorials provides 65 examples of
tangent functions in tabular and graph form.
3. Tutorial--Tangent Functions in Tabular and Graph Form: Example 01. In this
tutorial, construct a function table and graph for a tangent function of the form
y = tan(ax + b) with these characteristics: a = 1, b = 0.
4. Tutorial--Tangent Functions in Tabular and Graph Form: Example 02. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) with these characteristics: a > 1, b = 0.
5. Tutorial--Tangent Functions in Tabular and Graph Form: Example 03. In this
tutorial, construct a function table and graph for a tangent function of the
form y = tan(ax + b) with these characteristics: a < -1, b = 0.
6. Tutorial--Tangent Functions in Tabular and Graph Form: Example 04. In this
tutorial, construct a function table and graph for a tangent function of the
form y = tan(ax + b) with these characteristics: 0 < a < 1, b = 0.
7. Tutorial--Tangent Functions in Tabular and Graph Form: Example 05. In this
tutorial, construct a function table and graph for a tangent function of the
form y = tan(ax + b) with these characteristics: -1 < a < 0, b = 0.
8. Tutorial--Tangent Functions in Tabular and Graph Form: Example 06. In this
tutorial, construct a function table and graph for a tangent function of the
form y = tan(ax + b) with these characteristics: a = 1, b = π.
9. Tutorial--Tangent Functions in Tabular and Graph Form: Example 07. In this
tutorial, construct a function table and graph for a tangent function of the
form y = tan(ax + b) with these characteristics: a > 1, b = π.
10. Tutorial--Tangent Functions in Tabular and Graph Form: Example 08. In this
tutorial, construct a function table and graph for a tangent function of the
form y = tan(ax + b) with these characteristics: a < -1, b = π.
11. Tutorial--Tangent Functions in Tabular and Graph Form: Example 09. In this
tutorial, construct a function table and graph for a tangent function of the form
y = tan(ax + b) with these characteristics: 0 < a < 1, b = π.
12. Tutorial--Tangent Functions in Tabular and Graph Form: Example 10. In this
tutorial, construct a function table and graph for a tangent function of the form
y = tan(ax + b) with these characteristics: -1 < a < 0, b = π.
13. Tutorial--Tangent Functions in Tabular and Graph Form: Example 11. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) with these characteristics: a = 1, b = π/2.
14. Tutorial--Tangent Functions in Tabular and Graph Form: Example 12. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) with these characteristics: a > 1, b = π/2.
15. Tutorial--Tangent Functions in Tabular and Graph Form: Example 13. In this
tutorial, construct a function table and graph for a tangent function of the form
y = tan(ax + b) with these characteristics: a < -1, b = π/2.
16. Tutorial--Tangent Functions in Tabular and Graph Form: Example 14. In this
tutorial, construct a function table and graph for a tangent function of the form
y = tan(ax + b) with these characteristics: 0 < a < 1, b = π/2.
17. Tutorial--Tangent Functions in Tabular and Graph Form: Example 15. In this
tutorial, construct a function table and graph for a tangent function of the
form y = tan(ax + b) with these characteristics: -1 < a < 0, b = π/2.
18. Tutorial--Tangent Functions in Tabular and Graph Form: Example 16. In this
tutorial, construct a function table and graph for a tangent function of the form
y = tan(ax + b) + c with these characteristics: a = 1, b = 0, c = 1.
19. Tutorial--Tangent Functions in Tabular and Graph Form: Example 17. In this
tutorial, construct a function table and graph for a tangent function of the form
y = tan(ax + b) + c with these characteristics: a > 1, b = 0, c = 1.
20. Tutorial--Tangent Functions in Tabular and Graph Form: Example 18. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) + c with these characteristics: a < -1, b = 0, c = 1.
21. Tutorial--Tangent Functions in Tabular and Graph Form: Example 19. In this
tutorial, construct a function table and graph for a tangent function of the form
y = tan(ax + b) + c with these characteristics: 0 < a < 1, b = 0, c = 1.
22. Tutorial--Tangent Functions in Tabular and Graph Form: Example 20. In this
tutorial, construct a function table and graph for a tangent function of the form
y = tan(ax + b) + c with these characteristics: -1 < a < 0, b = 0, c = 1.
23. Tutorial--Tangent Functions in Tabular and Graph Form: Example 21. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) + c with these characteristics: a = 1, b = π, c = 1.
24. Tutorial--Tangent Functions in Tabular and Graph Form: Example 22. In this
tutorial, construct a function table and graph for a tangent function of the form
y = tan(ax + b) + c with these characteristics: a > 1, b = π, c = 1.
25. Tutorial--Tangent Functions in Tabular and Graph Form: Example 23. In this
tutorial, construct a function table and graph for a tangent function of the form
y = tan(ax + b) + c with these characteristics: a < -1, b = π, c = 1.
26. Tutorial--Tangent Functions in Tabular and Graph Form: Example 24. In this
tutorial, construct a function table and graph for a tangent function of the form
y = tan(ax + b) + c with these characteristics: 0 < a < 1, b = π, c = 1.
27. Tutorial--Tangent Functions in Tabular and Graph Form: Example 25. In this
tutorial, construct a function table and graph for a tangent function of the form
y = tan(ax + b) + c with these characteristics: -1 < a < 0, b = π, c = 1.
28. Tutorial--Tangent Functions in Tabular and Graph Form: Example 26. In this
tutorial, construct a function table and graph for a tangent function of the form
y = tan(ax + b) + c with these characteristics: a = 1, b = π/2, c = 1.
29. Tutorial--Tangent Functions in Tabular and Graph Form: Example 27. In this
tutorial, construct a function table and graph for a tangent function of the form
y = tan(ax + b) + c with these characteristics: a > 1, b = π/2, c = 1.
30. Tutorial--Tangent Functions in Tabular and Graph Form: Example 28. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) + c with these characteristics: a < -1, b = π/2, c = 1.
31. Tutorial--Tangent Functions in Tabular and Graph Form: Example 29. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) + c with these characteristics: 0 < a < 1, b = π/2, c = 1.
32. Tutorial--Tangent Functions in Tabular and Graph Form: Example 30. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) + c with these characteristics: -1 < a < 0, b = π/2, c = 1.
33. Tutorial--Tangent Functions in Tabular and Graph Form: Example 31. In this
tutorial, construct a function table and graph for a tangent function of the form y =
tan(ax + b) + c with these characteristics: a = 1, b = 0, c = -1.
34. Tutorial--Tangent Functions in Tabular and Graph Form: Example 32. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) + c with these characteristics: a > 1, b = 0, c = -1.
35. Tutorial--Tangent Functions in Tabular and Graph Form: Example 33. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) + c with these characteristics: a < -1, b = 0, c = -1.
36. Tutorial--Tangent Functions in Tabular and Graph Form: Example 34. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) + c with these characteristics: 0 < a < 1, b = 0, c = -1.
37. Tutorial--Tangent Functions in Tabular and Graph Form: Example 35. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) + c with these characteristics: -1 < a < 0, b = 0, c = -1.
38. Tutorial--Tangent Functions in Tabular and Graph Form: Example 36. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) + c with these characteristics: a = 1, b = π, c = -1.
39. Tutorial--Tangent Functions in Tabular and Graph Form: Example 37. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) + c with these characteristics: a > 1, b = π, c = -1.
40. Tutorial--Tangent Functions in Tabular and Graph Form: Example 38. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) + c with these characteristics: a < -1, b = π, c = -1.
41. Tutorial--Tangent Functions in Tabular and Graph Form: Example 39. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) + c with these characteristics: 0 < a < 1, b = π, c = -1.
42. Tutorial--Tangent Functions in Tabular and Graph Form: Example 40. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) + c with these characteristics: -1 < a < 0, b = π, c = -1.
43. Tutorial--Tangent Functions in Tabular and Graph Form: Example 41. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) + c with these characteristics: a = 1, b = π/2, c = -1.
44. Tutorial--Tangent Functions in Tabular and Graph Form: Example 42. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) + c with these characteristics: a > 1, b = π/2, c = -1.
45. Tutorial--Tangent Functions in Tabular and Graph Form: Example 43. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) + c with these characteristics: a < -1, b = π/2, c = -1.
46. Tutorial--Tangent Functions in Tabular and Graph Form: Example 44. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) + c with these characteristics: 0 < a < 1, b = π/2, c = -1.
47. Tutorial--Tangent Functions in Tabular and Graph Form: Example 45. In this
tutorial, construct a function table and graph for a tangent function of the form y
= tan(ax + b) + c with these characteristics: -1 < a < 0, b = π/2, c = -1.
48. Tutorial--Tangent Functions in Tabular and Graph Form: Example 46. In this
tutorial, construct a function table and graph for a tangent function of the form y
= a * tan(bx + c) + d with these characteristics: b = 1, c = 0, d = -1, a > 1.
49. Tutorial--Tangent Functions in Tabular and Graph Form: Example 47. In this
tutorial, construct a function table and graph for a tangent function of the form y
= a * tan(bx + c) + d with these characteristics: b > 1, c = 0, d = -1, a > 1.
50. Tutorial--Tangent Functions in Tabular and Graph Form: Example 48. In this
tutorial, construct a function table and graph for a tangent function of the form y
= a * tan(bx + c) + d with these characteristics: b < -1, c = 0, d = -1, a > 1.
51. Tutorial--Tangent Functions in Tabular and Graph Form: Example 49. In this
tutorial, construct a function table and graph for a tangent function of the form y
= a * tan(bx + c) + d with these characteristics: 0 < b < 1, c = 0, d = -1, a > 1.
52. Tutorial--Tangent Functions in Tabular and Graph Form: Example 50. In this
tutorial, construct a function table and graph for a tangent function of the form y
= a * tan(bx + c) + d with these characteristics: -1 < b < 0, c = 0, d = -1, a > 1.
53. Tutorial--Tangent Functions in Tabular and Graph Form: Example 51. In this
tutorial, construct a function table and graph for a tangent function of the form y
= a * tan(bx + c) + d with these characteristics: b = 1, c = π, d= -1, a > 1.
54. Tutorial--Tangent Functions in Tabular and Graph Form: Example 52. In this
tutorial, construct a function table and graph for a tangent function of the form y
= a * tan(bx + c) + d with these characteristics: b > 1, c = π, d = -1, a > 1.
55. Tutorial--Tangent Functions in Tabular and Graph Form: Example 53. In this
tutorial, construct a function table and graph for a tangent function of the form y
= a * tan(bx + c) + d with these characteristics: b < -1, c = π, d = -1, a > 1.
56. Tutorial--Tangent Functions in Tabular and Graph Form: Example 54. In this
tutorial, construct a function table and graph for a tangent function of the form y
= a * tan(bx + c) + d with these characteristics: 0 < b < 1, c = π, d = -1, a > 1.
57. Tutorial--Tangent Functions in Tabular and Graph Form: Example 55. In this
tutorial, construct a function table and graph for a tangent function of the form y
= a * tan(bx + c) + d with these characteristics: -1 < b < 0, c = π, d = -1, a > 1.
58. Tutorial--Tangent Functions in Tabular and Graph Form: Example 56. In this
tutorial, construct a function table and graph for a tangent function of the form y
= a * tan(bx + c) + d with these characteristics: b = 1, c = 0, d = -1, a < -1.
59. Tutorial--Tangent Functions in Tabular and Graph Form: Example 57. In this
tutorial, construct a function table and graph for a tangent function of the form y
= a * tan(bx + c) + d with these characteristics: b > 1, c = 0, d = -1, a < -1.
60. Tutorial--Tangent Functions in Tabular and Graph Form: Example 58. In this
tutorial, construct a function table and graph for a tangent function of the form y
= a * tan(bx + c) + d with these characteristics: b < -1, c = 0, d = -1, a < -1.
61. Tutorial--Tangent Functions in Tabular and Graph Form: Example 59. In this
tutorial, construct a function table and graph for a tangent function of the form y
= a * tan(bx + c) + d with these characteristics: 0 < b < 1, c = 0, d = -1, a < -1.
62. Tutorial--Tangent Functions in Tabular and Graph Form: Example 60. In this
tutorial, construct a function table and graph for a tangent function of the form y
= a * tan(bx + c) + d with these characteristics: -1 < b < 0, c = 0, d = -1, a < -1.
63. Tutorial--Tangent Functions in Tabular and Graph Form: Example 61. In this
tutorial, construct a function table and graph for a tangent function of the form y
= a * tan(bx + c) + d with these characteristics: b = 1, c = π, d = -1, a < -1.
64. Tutorial--Tangent Functions in Tabular and Graph Form: Example 62. In this
tutorial, construct a function table and graph for a tangent function of the form y
= a * tan(bx + c) + d with these characteristics: b > 1, c = π, d = -1, a < -1.
65. Tutorial--Tangent Functions in Tabular and Graph Form: Example 63. In this
tutorial, construct a function table and graph for a tangent function of the form y
= a * tan(bx + c) + d with these characteristics: b < -1, c = π, d = -1, e < -1.
66. Tutorial--Tangent Functions in Tabular and Graph Form: Example 64. In this
tutorial, construct a function table and graph for a tangent function of the form y
= a * tan(bx + c) + d with these characteristics: 0 < b < 1, c = π, d = -1, a < -1.
67. Tutorial--Tangent Functions in Tabular and Graph Form: Example 65. In this
tutorial, construct a function table and graph for a tangent function of the form y
= a * tan(bx + c) + d with these characteristics: -1 < b < 0, c = π, d = -1, a < -1.