the function, f(x), is plotted as shown. evaluate the following limits: lim x→−1 f(x)= lim x→1 f(x)= what is…

Explanation:

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

As $x$ approaches $-1$ from the left side, the function values approach $3$. So, $\lim_{x\to - 1^{-}}f(x)=3$.

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

As $x$ approaches $-1$ from the right side, the function values approach $3$. So, $\lim_{x\to - 1^{+}}f(x)=3$.

Step3: Find function value at $x = 1$

Looking at the graph, when $x = 1$, the function value $f(1)$ is not defined (there is an open - circle at $x = 1$). We can say $f(1)$ is undefined.

Answer:

$\lim_{x\to - 1^{-}}f(x)=3$ $\lim_{x\to - 1^{+}}f(x)=3$ $f(1)$ is undefined