the graph below is the function. determine the following values. enter \dne\ if a value does not exist…

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. $lim_{x\rightarrow1^{-}}f(x)=$ $lim_{x\rightarrow1^{+}}f(x)=$ $lim_{x\rightarrow1}f(x)=$ $f(1)=$

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. $lim_{x\rightarrow1^{-}}f(x)=$ $lim_{x\rightarrow1^{+}}f(x)=$ $lim_{x\rightarrow1}f(x)=$ $f(1)=$

Answer

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)