calc notes lecture 3

calc notes lecture 3 - (b) 1 , 1 1, 1 x x y x x-< =-A...

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Lecture Section s Objective Assignment 3 1.4 Domains, ranges of functions 1.4: 1-7 odds, 17-29 odds, 37, 39, 41, 47-57 odds Evaluate functions, inverse functions Understanding Goals: 1. To understand the definition of functions and know how to find the domains and ranges of functions. 2. To be able to determine whether a relation between two variables is a function or not. 3. To be able to evaluate functions and combine functions to create other functions. 4. To understand the definition of inverse functions and to find inverse functions algebraically. Example 1 : Which of the equations below define y as a function of x ? Explain your answer. a) 4 x y + = b) 2 2 4 x y + = c) 2 4 x y + = d) 2 4 x y + = 1
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Vertical line test: If every vertical line intersects the graph of an equation at most once, then the equation defines y as a function of x . Example 2 : Find the domain and range of each function. (a) 1 y x = -
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Unformatted text preview: (b) 1 , 1 1, 1 x x y x x-< =-A function is one-to-one if to each value of the dependent variable in the range there corresponds exactly one value of the independent variable. Horizontal line test: If every horizontal line intersects the graph of the function at most once, then the function is one-to-one. Note: The graph of a one-to-one function must satisfy both the vertical line test and the horizontal line test. 2 Function notation: ( ) f x- read as f of x . Example 3 : Let 2 ( ) 2 1 f x x x =--, find (a) ( ) f x x + V (b) ( ) ( ) f x x f x x +-V V Example 4 : Let ( ) 2 3 f x x =-and 2 ( ) 1 g x x = + , find a) ( ( )) f g x b) ( ( )) g f x 3 The graphs of f and 1 f-are mirror images of each other with respect to the line y x = . Example 5 : Find the inversion function of ( ) 2 1 f x x =-. 4...
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This note was uploaded on 04/17/2008 for the course MAT 111 taught by Professor Fan during the Spring '08 term at Union.

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calc notes lecture 3 - (b) 1 , 1 1, 1 x x y x x-< =-A...

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