Question

use the graph to answer the question.
identify all of the asymptotes for the graphed function. select all that apply.
(2 points)
$x = 2$
$x = 0$
$x = -2$
$y = 2$
$y = 0$

Explanation:

Step1: Recall the definition of vertical asymptote

Vertical asymptote is a vertical line \(x = a\) where the function approaches infinity or negative infinity as \(x\) approaches \(a\).

Step2: Analyze the graph

From the graph, we can see that as \(x\) approaches \(2\) and \(x\) approaches \(- 2\), the function values go to negative infinity. So \(x = 2\) and \(x=-2\) are vertical asymptotes.

Step3: Recall the definition of horizontal asymptote

Horizontal asymptote is a horizontal line \(y = b\) where \(\lim_{x
ightarrow\pm\infty}f(x)=b\).

Step4: Analyze the horizontal behavior

As \(x
ightarrow\pm\infty\), the function values approach \(y = 0\). So \(y = 0\) is a horizontal asymptote.

Answer:

\(x = 2\), \(x=-2\), \(y = 0\)