Question

question 22
write the equation of the asymptote(s) for the function graphed below. enter \dne\ in the answer blank if
does not exist.
vertical asymptote:
horizontal asymptote:
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Explanation:

Step1: Identify vertical asymptote

A vertical asymptote is a vertical line \(x = a\) where the function approaches infinity or negative infinity as \(x\) approaches \(a\). Looking at the graph, as \(x\) approaches \(-2\) from the left and right, the function values go to positive and negative infinity. So the vertical asymptote is \(x=-2\).

Step2: Identify horizontal asymptote

A horizontal asymptote is a horizontal line \(y = b\) that the function approaches as \(x\to\pm\infty\). As \(x\to\pm\infty\), the function approaches \(y = 0\). So the horizontal asymptote is \(y = 0\).

Answer:

Vertical Asymptote: \(x=-2\)
Horizontal Asymptote: \(y = 0\)