Question

what is the vertical asymptote of the function?

\\(x = -3\\)
\\(x = -2\\)
\\(x = 0\\)
\\(x = 3\\)

Explanation:

⚡ Using what you learned: Identifying Restrictions and Asymptotes

Step 1: Identify the vertical boundary line

A vertical asymptote is a vertical line \(x = c\) that the graph of a function approaches but never touches or crosses as the function values head toward positive or negative infinity.

Looking at the given graph, there is a vertical dashed line where the curve splits and heads sharply upward on the right and downward on the left.

Step 2: Determine the x-value of the asymptote

By counting the grid units along the x-axis:

• The origin is at \((0,0)\).
• The vertical dashed line passes through the x-axis at \(x = 3\).

Therefore, the equation of the vertical asymptote is:

$$x = 3$$

Answer:

\(x = 3\)