use the graph of the function f shown to estimate the following limits and the function value. complete…

Explanation:

Step1: Analyze left - hand limit as $x\to2^{-}$

Approach $x = 2$ from the left side on the graph. Observe the $y$ - value the function approaches.

Step2: Analyze right - hand limit as $x\to2^{+}$

Approach $x = 2$ from the right side on the graph. Observe the $y$ - value the function approaches.

Step3: Analyze overall limit as $x\to2$

The overall limit as $x\to2$ exists if and only if the left - hand limit and the right - hand limit are equal.

Step4: Analyze function value at $x = 2$

Locate the point on the graph where $x = 2$ to find $f(2)$.

Since the graph is not provided in a way that we can precisely read values, assume we have a graph where: (A) If the left - hand limit as $x\to2^{-}$ is $3$ (by observing the graph approaching $x = 2$ from the left), then $\lim_{x\to2^{-}}f(x)=3$. (B) If the right - hand limit as $x\to2^{+}$ is $1$ (by observing the graph approaching $x = 2$ from the right), then $\lim_{x\to2^{+}}f(x)=1$. (C) Since $\lim_{x\to2^{-}}f(x)\neq\lim_{x\to2^{+}}f(x)$, $\lim_{x\to2}f(x)$ does not exist. (D) If there is a closed - circle at $x = 2$ with $y = 1$, then $f(2)=1$.

Answer:

(A) $\lim_{x\to2^{-}}f(x)=3$ (B) $\lim_{x\to2^{+}}f(x)=1$ (C) The limit does not exist. (D) $f(2)=1$ (assuming the above - described graph features)