T04_Functions_and_Graphs - Mathematics Department(MD Centre...

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PMC 0045 Pre-Calculus for Engineering Foundation in Engineering ONLINE NOTES Topic 4 Functions and Graphs FOSEE , MULTIMEDIA UNIVERSITY (436821-T) MELAKA CAMPUS, JALAN AYER KEROH LAMA, 75450 MELAKA, MALAYSIA. Tel 606 252 3594 Fax 606 231 8799 URL: http://fosee.mmu.edu.my/~asd/ Mathematics Department (MD) Centre for Foundation Studies and Extension Education (FOSEE)
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PMC0045 Pre-Calculus for Engineering Topic 4 TOPIC 4: FUNCTIONS AND GRAPHS References : 1. Sullivan, M. (2002 ), Algebra & Trigonometry , 6 th Ed., Prentice Hall. 2. Blitzer, R., Goh Wei Wei, et.al. (2005), Algebra & Trigonometry , Prentice Hall. Objectives: 1. Identify functions and graph the functions using graphing techniques. 2. Identify the properties and characteristics of important functions. 3. Identify the characteristics of the inverse functions. Contents: 4.1 Basic of Functions 4.2 Graphs of Functions 4.3 Transformations of Functions 4.4 Combinations of Functions; Composite Functions 4.5 Inverse Functions 4.1 BASIC OF FUNCTIONS Definition: A function is defined as a corresponding from a set X of real numbers x to a set Y of real numbers y where the number y is unique for a specific number of x . - Set X is called the domain of the function. - For each element x in X , the corresponding element y in Y is called the value of the function at x , or the image of x . - The set of all images of the elements of X is called the range . Ordered Pairs We may consider a function f as a set of ordered pairs ( x , y ) or ( x , f ( x )) in which no two pairs have the same first element and different second element. For ( 29 1 1 , y x and ( 29 2 2 , y x , if 2 1 2 1 y y x x = = Example: y 2 = x don't represent a function since we have (1 , 1) and (1 , -1). Function Notation ) ( x f y = - f is a symbol for the rule that defines the function. - x is the independent variable (argument); - y is the dependent variable (its values depend on the value of x ) .
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