Question

use the graph to find the following limits.
(a) $lim_{x
ightarrow - 1}f(x)$ (b) $lim_{x
ightarrow1}f(x)$
(a) find the one - sided limits.
$lim_{x
ightarrow - 1^{-}}f(x)=square$
$lim_{x
ightarrow - 1^{+}}f(x)=square$

Explanation:

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

As $x$ approaches $-1$ from the left side ($x\to - 1^{-}$), we look at the part of the graph where $x$ values are less than $-1$ and getting closer to $-1$. Following the curve, we see that 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 ($x\to - 1^{+}$), we look at the part of the graph where $x$ values are greater than $-1$ and getting closer to $-1$. Following the curve, we see that the $y$ - value approaches $2$. So, $\lim_{x\to - 1^{+}}f(x)=2$.

Answer:

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