Find the domain of the function and identify any vertical and horizontal asymptotes. f\left ( x...

Question:

Find the domain of the function and identify any vertical and horizontal asymptotes.

{eq}f\left ( x \right ) \ = \ \frac{2x^{2}}{x \ + \ 6} {/eq}

Obtaining the Asymptotes of a Rational Function:

The behavior of rational functions typically distinguished from their domain and 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. They are obtained through division of the leading coefficient of the highest term in the numerator by the leading coefficient of the highest term in the denominator.

Answer and Explanation:

The domain of the given rational function is the set of all x-values that won't make the function undefined. Hence, the condition must be that the...

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Analyzing the Graph of a Rational Function: Asymptotes, Domain, and Range

from Math 105: Precalculus Algebra

Chapter 4 / Lesson 9
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