the function, f(x), is plotted as shown. evaluate each limit, if it exists. lim x→−1− f(x)= lim x→1+ f(x)=…

Explanation:

Step1: Analyze left - hand limit as $x\to - 1$

As $x$ approaches $-1$ from the left side (values of $x$ less than $-1$), we look at the part of the graph to the left of $x = - 1$. The $y$-value approaches $2$. So, $\lim_{x\to - 1^{-}}f(x)=2$.

Step2: Analyze right - hand limit as $x\to - 1$

As $x$ approaches $-1$ from the right side (values of $x$ greater than $-1$), we look at the part of the graph to the right of $x=-1$. The $y$-value approaches $2$. So, $\lim_{x\to - 1^{+}}f(x)=2$.

Step3: Analyze overall limit as $x\to - 1$

Since $\lim_{x\to - 1^{-}}f(x)=\lim_{x\to - 1^{+}}f(x) = 2$, then $\lim_{x\to - 1}f(x)=2$.

Answer:

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