Question

Use the graph of the rational function to complete the following statement.
As x right arrow minus 1 Superscript minus​, f left parenthesis x right parenthesis right arrow Modifying with underline.
-5
5
-3
3
x
y



A coordinate system has a horizontal x-axis labeled from negative 5 to 5 in increments of 1 and a vertical y-axis labeled from negative 3 to 3 in increments of 1. A graph has three branches and asymptotes x = negative 1 and x = 1. The first branch is above the x-axis and to the left of x = negative 1, approaching both. The second branch rises from left to right between the asymptotes, passing through (0, 0). The third branch is below the x-axis and to the right of x = 1, approaching both.
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Part 1
As x right arrow minus 1 Superscript minus​, f left parenthesis x right parenthesis right arrow
  
enter your response here.

Answer 1

To answer this question, we need to analyze the behavior of the rational function as \( x \) approaches \(-1\) from the left (denoted as \( x \rightarrow -1^{-} \)).

Given the description of the graph, we know:
- There is a vertical asymptote at \( x = -1 \).
- The first branch of the graph, which is to the left of the vertical asymptote \( x = -1 \), approaches both the x-axis and the vertical asymptote as \( x \) approaches \(-1\).

Since the branch is above the x-axis and approaches the vertical asymptote from the left, the function \( f(x) \) will approach \( +\infty \) as \( x \) approaches \(-1\) from the left.

Thus, we conclude:

As \( x \rightarrow -1^{-}, f(x) \rightarrow +\infty \).