Question

use the graph of the rational function to complete the following statement. as x → 4⁺, f(x) → ____.

Explanation:

Step1: Analyze the graph near \( x = 4^+ \)

We look at the behavior of the function \( f(x) \) as \( x \) approaches \( 4 \) from the right (denoted as \( x \to 4^+ \)). From the graph, we observe the vertical asymptote or the trend of the curve near \( x = 4 \) on the right - hand side.

Step2: Determine the limit

As \( x \) gets closer to \( 4 \) from values greater than \( 4 \) (i.e., \( x \to 4^+ \)), we can see from the graph that the function values are going downwards without bound. In other words, the function \( f(x) \) approaches \( -\infty \) as \( x \to 4^+ \).

Answer:

\( -\infty \)