Question

use the graph to determine the equations of the vertical asymptote. l commas: x = question help: video message instructor

Explanation:

Step1: Recall vertical asymptote definition

A vertical asymptote is a vertical line \( x = a \) where the function approaches \( \pm\infty \) as \( x \) approaches \( a \) from the left or right.

Step2: Analyze the graph

Look at the graph: there are vertical lines (asymptotes) where the function has infinite behavior. From the grid, the vertical asymptotes are at \( x = -2 \) and \( x = 2 \)? Wait, no, wait the graph: the left vertical asymptote is at \( x = -2 \)? Wait, no, looking at the graph, the vertical asymptotes are at \( x = -2 \) and \( x = 2 \)? Wait, no, let's check the x - coordinates. The graph has vertical asymptotes at \( x=-2 \) and \( x = 2 \)? Wait, no, the lower part: the vertical lines are at \( x=-2 \) and \( x = 2 \)? Wait, no, looking at the x - axis, the vertical asymptotes are at \( x=-2 \) and \( x = 2 \)? Wait, no, the graph shows that at \( x=-2 \) and \( x = 2 \), the function has vertical asymptotes (the blue lines go to infinity there). Wait, but maybe I misread. Wait, the x - axis labels: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. The vertical asymptotes are at \( x=-2 \) and \( x = 2 \)? Wait, no, the left vertical asymptote is at \( x=-2 \), and the right one at \( x = 2 \)? Wait, no, looking at the graph, the vertical asymptotes are at \( x=-2 \) and \( x = 2 \). Wait, but maybe the problem expects both? Wait, the input says "equations of the vertical asymptote" (maybe multiple). Wait, the graph: the upper curves have vertical asymptotes at \( x=-2 \) and \( x = 2 \)? Wait, no, let's check again. The vertical asymptotes are at \( x=-2 \) and \( x = 2 \). So the equations are \( x=-2 \) and \( x = 2 \).

Answer:

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