Question

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

Explanation:

Step1: Identify vertical asymptotes

Vertical asymptotes occur where the function approaches infinity. From the graph, the lower \(x -\)value vertical asymptote is at \(x = 1\) (as the function tends to infinity near this \(x -\)value).

Step2: Identify higher \(x -\)value vertical asymptote

The higher \(x -\)value vertical asymptote is at \(x = 3\) (as the function tends to infinity near this \(x -\)value).

Step3: Identify horizontal asymptote

A horizontal asymptote is a horizontal line \(y = k\) that the function approaches as \(x\to\pm\infty\). From the graph, as \(x\to\pm\infty\), the function approaches \(y = 2\).

Answer:

Vertical Asymptote (lower \(x -\)value): \(1\)
Vertical Asymptote (higher \(x -\)value): \(3\)
Horizontal Asymptote: \(2\)