Homework 11

# 4 3 2 1 0 1 2 3 4 5 6 explanation since x2 16 0 when

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Unformatted text preview: -1 -2 -3 -4 -5 -6 Explanation: Since x2 - 16 = 0 when x = 4, the graph of f will have vertical asymptotes at x = 4; on the other hand, since 4 2 -4 -2 -2 -4 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 x lim x2 = 1, x2 - 16 2 4 the graph will have a horizontal asymptote at y = 1. This already eliminates some of the possible graphs. On the other hand, f (0) = 0, so the graph of f must also pass through the origin. This eliminates another graph. To decide which of the remaining graphs is that of f we look at the sign of f to determine where f is increasing or decreasing. Now, by the Quotient Rule, f (x) = 2x(x2 - 16) - 2x3 (x2 - 16)2 = - Thus (x2 32x . - 16)2 6 5 5.4 3 2 1 0 -1 -2 -3 -4 -5 -6 4 2 -4 -2 -2 -4 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 2 4 while f (x) &gt; 0, x &lt; 0, f (x) &lt; 0, x &gt; 0, so the graph of f is increasing to the left of the origin and decreasing to the right of the origin. The only graph having all these properties is 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 Garcia, Ilse Homework 11 Due: Nov 6 2007, 3:00 am Inst: Fonken 4 2 -4 -2 -2 -4 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 2 4 Consequently, this must be the graph of f . keywords: graph, ration...
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## This note was uploaded on 01/16/2009 for the course M 408k taught by Professor Schultz during the Spring '08 term at University of Texas at Austin.

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