Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 3 - Review - Test - Page 323: 11

Answer

(a) $r(x),u(x)$ (b) $s(x)$ (c) $s(x),w(x)$ (d) $w(x)$ (e) $x=-1,2$ (vertical) and $y=0$ (horizontal) (f) see graph, symptotes $x=\pm5$, x-intercepts $-4.372, 1.372$, y-intercept $0.24$ (g) $P(x)=x^2-2x-5$

Work Step by Step

(a) as $x\to \pm \infty, r(x)\to 0, u(x)\to 1$ they both have horizontal asymptotes. (b) $s(x)$ will has a slant asymptote because the quotient will be a line. (c) $s(x)$ has no vertical asymptote because its divisor is always larger than 4, $w(x)$ has no vertical asymptote because the dividend contains a factor which is the same as the divisor. (d) $w(x)$ has a "hole" because both the dividend and the divisor has a common factor of $x+3$ (e) The asymptotes of function $r(x)$ are $x=-1,x=2$ (vertical) and $y=0$ (horizontal) (f) See graph, asymptotes are $x=\pm5$, x-intercepts $-3,2$, y-intercept $0.24$ (g) Using long division as shown in the figure (g), we can find the quotient of $t(x)$ as $x^2-2x-5$, let $P(x)=x^2-2x-5$ and plot both $P(x), t(x)$ and it can be seen that they have the same end behavior.
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