Question

use the graph of the rational function to complete the following statement. as x → -1⁻, f(x) → _____.

Explanation:

Step1: Understand the Notation

The notation \( x \to -1^{-} \) means we are looking at the behavior of the function \( f(x) \) as \( x \) approaches \( -1 \) from the left - hand side (values of \( x \) that are slightly less than \( -1 \)).

Step2: Analyze the Graph

Looking at the graph of the rational function, as \( x \) gets closer and closer to \( -1 \) from the left (moving towards \( -1 \) from values like \( -1.1, - 1.01, - 1.001,\cdots\)), we observe the vertical asymptote at \( x=-1 \) (the left - most vertical dashed line). From the left - hand side of \( x = - 1 \), the graph of the function is rising upwards. This means that as \( x\to - 1^{-}\), the function values \( f(x) \) are increasing without bound, which is represented as \( f(x)\to+\infty \) (or we can also say it approaches positive infinity).

Answer:

\(+\infty\) (or "positive infinity")