Question

use the graph of the rational function to complete the following statement.
as x → -4⁻, f(x) → ____.
as x → -4⁻, f(x) → \boxed{}.

Explanation:

Step1: Identify the vertical asymptote

The graph has vertical asymptotes at \( x = -4 \) and \( x = 4 \) (since the function approaches these lines but never touches them).

Step2: Analyze the left - hand limit as \( x \to - 4^{-} \)

When \( x \) approaches \( - 4 \) from the left (values slightly less than \( - 4 \)), we look at the part of the graph near \( x=-4 \) on the left side. The lower part of the graph (the curve below the x - axis) near \( x = - 4 \) (left of \( x=-4\)) is moving towards negative infinity as \( x \) gets closer to \( - 4 \) from the left. So as \( x\to - 4^{-} \), \( f(x)\to-\infty \).

Answer:

\(-\infty\)