Question

use the graph of the function f shown to the right to estimate the indicated function values and limits. complete parts (a) through (e). (c) find the value of lim f(x). select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. lim f(x)=
b. the limit does not exist.

Explanation:

Step1: Analyze left - hand limit

As \(x\) approaches \(- 2\) from the left side (\(x\to - 2^{-}\)), we look at the values of the function \(y = f(x)\) on the graph. Following the curve of the function as \(x\) gets closer to \(-2\) from the left, the \(y\) - value approaches \(2\).

Step2: Analyze right - hand limit

As \(x\) approaches \(- 2\) from the right side (\(x\to - 2^{+}\)), we look at the values of the function \(y = f(x)\) on the graph. Following the curve of the function as \(x\) gets closer to \(-2\) from the right, the \(y\) - value approaches \(2\).

Step3: Determine the limit

Since the left - hand limit \(\lim_{x\to - 2^{-}}f(x)=2\) and the right - hand limit \(\lim_{x\to - 2^{+}}f(x)=2\), then \(\lim_{x\to - 2}f(x)=2\).

Answer:

\(2\)