College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 3 - Polynomial and Rational Functions - Exercise Set 3.5 - Page 409: 111

Answer

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Work Step by Step

The vertical asymptote of a function $y = f(x)$ is a vertical line $x = k$ when $y\rightarrow\infty$ or $y\rightarrow -\infty$. Vertical Asymptotes From Graph By seeing the above examples, you might have already got an idea of determining the vertical asymptotes from a graph. If a part of the graph is turning to be vertical, then there might probably be a VA along that vertical line. The value of the function becomes $\infty$ or $-\infty$ at the value of $x$ along which you found the VA. But note that a vertical asymptote should never touch the graph. Vertical Asymptotes of Rational Function We do not need to use the concept of limits (which is a little difficult) to find the vertical asymptotes of a rational function. Instead, use the following steps: Step 1: Simplify the rational function. i.e., Factor the numerator and denominator of the rational function and cancel the common factors. Step 2: Set the denominator of the simplified rational function to zero and solve.
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