Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 2 - Nonlinear Functions - 2.3 Polynomial and Rational Functions - 2.3 Exercises - Page 75: 40

Answer

$$ y =\frac{9-6 x+x^{2}}{3-x} $$ There are no asymptotes, but there is a hole at $x=3$. There is no $x$-intercept, since $3-x$ implies $x=3$ but there is a hole at $x=3$ $y$-intercept: $3$ the value when $x= 0$.
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Work Step by Step

$$ y =\frac{9-6 x+x^{2}}{3-x} $$ To find a asymptote, let $$ \begin{aligned} y &=\frac{9-6 x+x^{2}}{3-x} \\ &=\frac{(3-x)(3-x)}{3-x} \\ &=3-x, x \neq 3 \end{aligned} $$ There are no asymptotes, but there is a hole at $x=3$. There is no $x$-intercept, since $3-x$ implies $x=3$ but there is a hole at $x=3$ $y$-intercept: $3$ the value when $x= 0$.
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