Question

use the graph of the rational function to complete the following statement. as ( x \to 1^+ ), ( f(x) \to ) ______. as ( x \to 1^+ ), ( f(x) \to square ).

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 right - hand side (values of \( x \) that are just greater than 1).

Step2: Analyze the graph

From the given graph of the rational function, we observe the vertical asymptote (the vertical blue line) around \( x = 1 \) (assuming the vertical asymptote is at \( x=1 \) from the context). When we approach \( x = 1 \) from the right ( \( x\to1^+ \) ), we look at the part of the graph that is to the right of \( x = 1 \). From the shape of the graph (the curve near the vertical asymptote at \( x = 1 \)), as \( x \) gets closer to 1 from values greater than 1, the function \( f(x) \) is going downwards without bound, which means \( f(x)\to-\infty \) (negative infinity).

Answer:

\( -\infty \)