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Pre-Calculus Practice Problem 56

Pre-Calculus Practice Problem 56 - Unit 2 Activity 2...

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Unit 2, Activity 2, Discovery using Technology with Answers Blackline Masters, Advanced Math-PreCalculus Page 54 Louisiana Comprehensive Curriculum, Revised 2008 1. Plot on the same screen the following graphs: , 2 x y = , 3 x y = y = x 4 , y = x 5 a) What points do all of the graphs have in common? All of the graphs pass through (0, 0) and (1, 1) b) Which function increases most rapidly, and which increases least rapidly, as x becomes large? y = x 5 increases most rapidly and y = x 2 increases least rapidly c) What are the main differences between the graphs of the even powers of x and the odd powers of x ? The graphs of the even powers of x are even functions; that is, they are symmetrical over the y-axis. The graphs of the odd powers of x are odd functions; that is, they are symmetrical around the origin. The end-behavior of the even powers is the same as x y x y → ∞ → ∞ → −∞ → ∞ , , and as . The same can be said for the end-behavior of the odd powers: as x y x y → ∞ → ∞ → −∞ → −∞ , , and as .
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