Post1o2_1330 - g. Which of the following points is also on...

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Section 1.2 – Functions and Graphs 1 Section 1.2 Functions and Graphs Vertical Line Test A curve is the graph of a function if and only if each vertical line intersects it in at most one point. Example 1: Determine whether the given graph is the graph of a function. A. B. Even and Odd Functions A function f is even if ) ( ) ( x f x f = - for all x in the domain of f . Since an even function is symmetric with respect to the y-axis, the points ) , ( y x - and ) , ( y x are on the same graph. This is the graph of the even function 2 ) ( x x f = . Notice that (-1, 1) and (1, 1) are on the graph. -3 -2 -1 1 2 3 -1 1 2 x y
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Section 1.2 – Functions and Graphs 2 A function f is odd if ) x ( f ) x ( f - = - for all x in the domain of f . Since an odd function is symmetric with respect to the origin, the points ) y , x ( - - and ) y , x ( are on the same graph. This is the graph of the odd function 3 x ) x ( f = . Notice that (-1, -1) and (1, 1) are on the graph. -3 -2 -1 1 2 3 -1 1 x y Example 2: Suppose that g(x) is an even function and that (-3, -7) is on the graph of
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Unformatted text preview: g. Which of the following points is also on the graph of g? A. (3, 7) B. (-7, -3) C. (-3, 7) D. (7, 3) E. (3, -7) Example 3: Determine if the following functions are odd, even, both, or neither. 2 4 3 5 ) ( x x x f-= Recall: Even: ) ( ) ( x f x f =-Odd: ) ( ) ( x f x f-=-Section 1.2 Functions and Graphs 3 A function is increasing on an interval whenever a b then ( ) ( ) f a f b (going uphill from left to right). A function is decreasing on an interval whenever a b then ( ) ( ) f a f b < (going downhill from left to right). Example 4: Given the following graph of a function: -4-3-2-1 1 2 3 4 5 6 7 8 9 10-2-1 1 2 3 4 5 x y a. What is the range of the function? b. Determine the intervals where the function is increasing. Increasing: c. Determine the y-intercept. Example 5: Suppose --+ = 3 x 10 , 2 x 3 x , 2 x ) x ( f . Find the domain....
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This note was uploaded on 02/20/2012 for the course MATH 1330 taught by Professor Staff during the Fall '08 term at University of Houston.

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Post1o2_1330 - g. Which of the following points is also on...

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