Question

find all horizontal asymptotes of the following function.

$f(x)=\frac{2x + 2}{x^{2}-x - 2}$

answer attempt 1 out of 2

one horizontal asymptote
no horizontal asymptotes
one horizontal asymptote
two horizontal asymptotes
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Explanation:

Step1: Analyze the degrees of numerator and denominator

The degree of the numerator \(2x + 2\) (where the highest - power term is \(2x\) with degree \(n = 1\)) and the degree of the denominator \(x^{2}-x - 2\) (where the highest - power term is \(x^{2}\) with degree \(m=2\)).

Step2: Apply the horizontal asymptote rule

When \(n\lt m\) (here \(n = 1\) and \(m = 2\)), the horizontal asymptote is \(y = 0\).

Answer:

One Horizontal Asymptote (\(y = 0\))