Unit 2, Activity 2,Discovery using Technology with Answers Blackline Masters, Advanced Math-PreCalculusPage 54 Louisiana Comprehensive Curriculum, Revised 20081. Plot on the same screen the following graphs: ,2xy=,3xy=y= x4, y= x5a) 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 xbecomes large? y = x5increases most rapidly and y = x2increases least rapidly c) What are the main differences between the graphs of the even powers of xand 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 asxyxy→ ∞→ ∞→ −∞→∞,,and as . The same can be said for the end-behavior of the odd powers: as xy→∞→ −−∞and as .
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This note was uploaded on 10/10/2011 for the course MAC 1147 taught by Professor German during the Fall '08 term at University of Florida.