# A 24 x b 5 8 x d d c 19 x example 5 mrs oliver throws

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(a) > @ 2,4 x (b) 5 8 x d d (c) > @ 1,9 x ± Example 5 Mrs. Oliver throws a Precalculus textbook from the top of a tall tower, the distance it has fallen after t seconds is given by the function 2 ( ) 16 d t t . Find the book’s average speed over the following intervals: (a) > @ 1,5 t (b) > @ , t a a h ² The average rate of change of the function ( ) y f x between x a and x b is ࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵? ࠵?࠵? ࠵?ℎ࠵?࠵?࠵?࠵? = ∆࠵? ∆࠵? = ࠵?(࠵?) − ࠵?(࠵?) ࠵? − ࠵? The above is called a difference quotient, and is the same difference quotient you learned in Algebra I when you were learning how to calculate slope. There is a graphical interpretation of this. The average rate of change is the slope of the secant line between x a and x b on the graph of f , that is, the line passing through the points ³ ´ , ( ) a f a and ³ ´ , ( ) b f b . Yz slope xz x i fadCx 412 5,8 flat zs fest 16 fcs l ftp.zsfczy ufcul O r A Roc f Csl fcs ARoc fca ffl AR0C t µ z s o o o y Arg dcs da Args _death dla s l ath a 4004 162 38,1 dCathl d h 96 Sec

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If you’ve ever drawn a line straight down the middle of your body from the top of your head to the floor the n looked in the mirror, you have realized how fun it can be to play with markers, but you’ve also realized that you posses s a vertical line of bilateral symmetry. If you folded yourself along your drawn line, after a few “ouches,” your right and left side would coincide nicely. Graphs have symmetries too! Example 6 Determine algebraically if the following functions are even, odd, or neither. Verify graphically if possible. (a) 2 ( ) 5 f x x ± ² (b) 2 ( ) 4 3 g x x x ± ² (c) 3 ( ) 2 3 h x x ± (d) 3 1 ( ) 2 v t t t ± ± (e) 3 2 ( ) 3 2 m r m m ± (f) 5 3 3 3 6 ( ) 3 4 z z z q z z z ± ² ² From the examples above, we can generalize some rules of thumbs about the symmetry of some types of functions based on the algebraic test of replacing x with ± x .

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