Question

the graph below is the function. determine the following values. enter \dne\ if a value does not exist, enter \oo\ (lower case \o\) if the limit approaches positive infinity, or \-oo\ if the limit approaches negative infinity. $lim_{x
ightarrow1^{-}}f(x)=$ $lim_{x
ightarrow1^{+}}f(x)=$ $lim_{x
ightarrow1}f(x)=$ $f(1)=$

Explanation:

Step1: Left - hand limit as x approaches 1

As \(x\) approaches \(1\) from the left side (\(x\to1^{-}\)), we look at the values of the function coming from the left. The graph approaches \(y = - 1\). So, \(\lim_{x\to1^{-}}f(x)=-1\).

Step2: Right - hand limit as x approaches 1

As \(x\) approaches \(1\) from the right side (\(x\to1^{+}\)), we look at the values of the function coming from the right. The graph approaches \(y=-1\). So, \(\lim_{x\to1^{+}}f(x)=-1\).

Step3: Overall limit as x approaches 1

Since \(\lim_{x\to1^{-}}f(x)=\lim_{x\to1^{+}}f(x)=-1\), then \(\lim_{x\to1}f(x)=-1\).

Step4: Value of the function at x = 1

The solid dot on the graph at \(x = 1\) is at \(y = 2\). So, \(f(1)=2\).

Answer:

\(\lim_{x\to1^{-}}f(x)=-1\)
\(\lim_{x\to1^{+}}f(x)=-1\)
\(\lim_{x\to1}f(x)=-1\)
\(f(1)=2\)