Let f(x) =\frac{5x^2 + 1}{4 - x^2}. Determine the vertical and horizontal asymptotes of f.

Question:

Let f(x) = {eq}\frac{5x^2 + 1}{4 - x^2}. {/eq} Determine the vertical and horizontal asymptotes of f.

Obtaining the Asymptotes of a Rational Function:

The behavior of rational functions are sometimes distinguished from their asymptotes. Asymptotes are lines that are very close to a curve yet does not touch it. They are common in rational functions due to the restrictions in the domain of the function. Vertical asymptotes are achieved by equating the denominator to zero. Meanwhile, horizontal asymptotes are present when the highest exponent in the numerator is the same as the denominator. Lastly, oblique asymptotes will be observed if the highest exponent in the numerator is greater than the highest exponent in the denominator.

Answer and Explanation:

To obtain the vertical asymptotes, we set the denominator of the rational expression to be equal to zero. So

{eq}\begin{align} 4 - x^2 &=...

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Graphing & Analyzing Rational Functions

from Precalculus: High School

Chapter 13 / Lesson 2
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