Question

use the graph of the rational function to complete the following statement. as x → 3⁻, f(x) → ____ . as x → 3⁻, f(x) → \boxed{}.

Explanation:

Step1: Understand the Notation

The notation \( x \to 3^- \) means we are looking at the behavior of the function \( f(x) \) as \( x \) approaches 3 from the left - hand side (values of \( x \) that are slightly less than 3).

Step2: Analyze the Graph

Looking at the graph of the rational function, we observe the vertical asymptote (the blue vertical line) near \( x = 3 \). When we approach \( x = 3 \) from the left (values like \( 2.9, 2.99, 2.999,\cdots \)), we need to see the trend of the \( y \) - values (the values of \( f(x) \)). From the graph, as \( x \) gets closer and closer to 3 from the left, the function values (the \( y \) - coordinates of the points on the graph) are decreasing without bound, which means they are approaching negative infinity.

Answer:

\( -\infty \)