Types of functions and their domain & range - mohd noor
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This document defines and provides examples of constant and linear functions. A constant function has values that do not vary, with examples given by y=5 and x=50. A linear function is a first degree polynomial of one variable in the form of y=mx+c, where m is the slope and c is the y-intercept. Linear functions are represented by straight lines that can be skewed left if m<0 or right if m>0. Examples of linear functions and their domains and ranges are given.
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The process of making a decisionMohd. Noor Abdul Hamid This document discusses decision making methods and factors that influence decision making. It describes the Kepner-Tregoe decision making method which involves defining the problem, generating alternatives, establishing objectives, evaluating alternatives against objectives, and making a final choice. It also discusses how psychological types, culture, and decision structure (structured, semi-structured, unstructured) can impact decision making.
Introduction to DSS
Introduction to DSSMohd. Noor Abdul Hamid This document provides an overview of decision support systems (DSS), including their history, evolution, definitions, components, users, and categories. It discusses how DSS have developed from early computers used for calculations during World War II to today's data-driven systems. A DSS is defined as an information system that provides knowledge workers with information to make informed decisions. Key components of a DSS include a database, model base, knowledge base, and user interface. DSS support but do not replace human decision makers such as executives and managers. Common categories of DSS are data-driven versus model-driven and individual versus group-oriented systems.
Classification Using Decision tree
Classification Using Decision treeMohd. Noor Abdul Hamid The document provides an introduction to classification techniques in machine learning. It defines classification as assigning objects to predefined categories based on their attributes. The goal is to build a model from a training set that can accurately classify previously unseen records. Decision trees are discussed as a popular classification technique that recursively splits data into more homogeneous subgroups based on attribute tests. The document outlines the process of building decision trees, including selecting splitting attributes, stopping criteria, and evaluating performance on a test set. Examples are provided to illustrate classification tasks and building a decision tree model.
Decision tree Using c4.5 Algorithm
Decision tree Using c4.5 AlgorithmMohd. Noor Abdul Hamid The document describes the C4.5 algorithm for building decision trees. It begins with an overview of decision trees and the goals of minimizing tree levels and nodes. It then outlines the steps of the C4.5 algorithm: 1) Choose the attribute that best differentiates training instances, 2) Create a tree node for that attribute and child nodes for each value, 3) Recursively create subordinate nodes until reaching criteria or no remaining attributes. An example applies these steps to build a decision tree to predict customers' responses to a life insurance promotion using attributes like age, income and insurance status.
Limit - Mohd Noor
Limit - Mohd NoorMohd. Noor Abdul Hamid This document discusses how to calculate limits of functions as the input value approaches a given number. It explains how to build left and right tables to determine one-sided limits and check if the left and right limits are equal to determine if the overall limit exists. It also discusses special cases for calculating limits of rational functions and limits as the input approaches infinity. The key steps are to identify the terms with the highest powers, eliminate lesser terms, simplify, and substitute the given input value.
Lagrange Multiplier - Mohd Moor
Lagrange Multiplier - Mohd MoorMohd. Noor Abdul Hamid This document discusses maximizing production levels for t-shirts and pants given constraints. It introduces Mohd Noor Abdul Hamid and provides his contact information. The level of production is defined by an equation using variables x for t-shirts and y for pants. The objective is to maximize production and the constraint is that 1.5x + 2y must equal 250 meters of fabric.
Introduction to Exponential Function - Mohd noor
Introduction to Exponential Function - Mohd noorMohd. Noor Abdul Hamid To cut a pizza into 8 equal pieces with 3 cuts:
1) Cut the pizza in half, making 2 pieces.
2) Stack the 2 pieces and cut again, making 4 pieces.
3) Stack the 4 pieces and cut again, making the final 8 pieces.
The number of pieces grows exponentially based on the number of cuts, following the formula N = 2c, where N is the number of pieces and c is the number of cuts.
Domain & Range (from graph) - Mohd Noor
Domain & Range (from graph) - Mohd NoorMohd. Noor Abdul Hamid This slide demonstrates how you can obtain the domain and range of a particular function based on its graph.
Differentiation using First Principle - By Mohd Noor Abdul Hamid
Differentiation using First Principle - By Mohd Noor Abdul HamidMohd. Noor Abdul Hamid 1. The document discusses the concept of the derivative and differentiation using the first principle. It explains how to calculate the slope of a tangent line to a curve at a point using limits, which gives the derivative of the function at that point.
2. Rules for differentiating common functions like polynomials, exponentials, and logarithms are covered. Higher-order derivatives and applications of derivatives to business and economics are also mentioned.
3. The goals of the class are to explain the concept of the derivative, differentiate functions using the first principle (limits), and understand various differentiation rules.
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- 1. Mohd Noor Abdul Hamid, Ph.D
- 2. 1. CONSTANT FUNCTION • a function whose values do not vary and thus are constant Eg 1: y = 5 Domain = { x ε R } -∞ +∞ 5 Range = { y = 5 }
- 3. 1. CONSTANT FUNCTION • a function whose values do not vary and thus are constant Eg 2: x= 50 Domain = { x = 50 } Range = { y ε R } 50 +∞ -∞
- 4. 2. LINEAR FUNCTION • a first degree polynomial function of one variable y = f(x) = mx + c slope / gradient y-intercept • graph : straight lines. - skewed to the left m < 0 - skewed to the right m > 0
- 5. 2. LINEAR FUNCTION Example 1 : y = 2x + 4 -∞ +∞ Domain = { x ε R } +∞ -∞ Range = { y ε R }
- 6. 2. LINEAR FUNCTION Example 1 : y = -5x + 10 -∞ +∞ Domain = { x ε R } -∞ +∞ Range = { y = R }