Question

determine the horizontal or slant asymptote of the following function. enter any asymptote as an equation. if there is neither a horizontal asymptote nor slant asymptote, enter none.

$f(x)=\frac{2x^{3}+4x^{2}-16x}{x^{2}-1}$

Explanation:

Step1: Divide the numerator by the denominator

Use polynomial long - division. Divide \(2x^{3}+4x^{2}-16x\) by \(x^{2}-1\).

$$
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$$

Step2: Analyze the remainder term

As \(x\to\pm\infty\), \(\frac{-4}{x^{2}-1}\to0\).

Answer:

The slant asymptote is \(y=2x+4\).