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PP Section 3.3

# PP Section 3.3 - Shapes of Graphs Average Rate of Change A...

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Shapes of Graphs Average Rate of Change

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A function f is even if for every number x in its domain the number -x is also in the domain and f(x) = f(-x). A function is even if and only if its graph is symmetric with respect to the y -axis. A function f is odd if for every number x in its domain the number -x is also in the domain and - f(x) = f(-x). A function is odd if and only if its graph is symmetric with respect to the origin.
Example of an Even Function. It is symmetric about the y-axis x y (0,0) x y (0,0) Example of an Odd Function. It is symmetric about the origin

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Determine whether each of the following functions is even, odd, or neither. Then determine whether the graph is symmetric with respect to the y -axis or with respect to the origin. 2 ) ( 2 + - = z z g a.) 2 2 ) ( ) ( 2 2 + - = + - - = - z z z g g z g z ( ) ( ) = - Even function, graph symmetric with respect to the y -axis. 2 ) ( 2 + - = z z g
x x x f 3 4 ) ( 5 + - = b.) f x x x x x ( ) ( ) ( ) - = - - + - = - 4 3 4 3 5 5 f x f x ( ) ( ) - Not an even function. - = - - + = - f x x x x x ( ) ( ) 4 3 4 3 5 5 f x x x x x ( ) ( ) ( ) - = - - + - = - 4 3 4 3 5 5 f x f x ( ) ( ) - = - Odd function, and the graph is symmetric with respect to the origin.

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