Question

write the equation of the asymptote(s) for the function graphed below. enter \dne\ in the answer blank if an asymptote does not exist. vertical asymptote: horizontal asymptote: question help: post to forum

Explanation:

Step1: Identify vertical asymptote

A vertical asymptote occurs where the function approaches infinity or negative infinity. Looking at the graph, there is no such \(x -\)value where the function behaves this way. So vertical asymptote: \(DNE\)

Step2: Identify horizontal asymptote

A horizontal asymptote is a \(y -\)value that the function approaches as \(x\to\pm\infty\). As \(x\to\pm\infty\), the function approaches \(y = 2\). So horizontal asymptote: \(y=2\)

Answer:

Vertical Asymptote: \(DNE\)
Horizontal Asymptote: \(y = 2\)