Using the graph, find the specified limit or state that the limit does not exist (DNE).
${\lim }_{x\to -2^{-}}f\left(x\right)$, ${\lim }_{x\to -2^{+}}f\left(x\right)$, ${\lim }_{x\to -2^{}}f\left(x\right)$

• A. ${\lim }_{x\to -2^{-}}-f\left(x\right)=1,{\lim }_{x\to -2^{+}}f\left(x\right)=1,{\lim }_{x\to -2}f\left(x\right)=1$
• B. ${\lim }_{x\to -2^{-}}f\left(x\right)=1,{\lim }_{x\to -2^{+}}f\left(x\right)=-1,{\lim }_{x\to -2}f\left(x\right)=DNE$
• C. ${\lim }_{x\to -2^{-}}f\left(x\right)=1,{\lim }_{x\to -2^{+}}f\left(x\right)=1,{\lim }_{x\to -2}f\left(x\right)=DNE$
• D. ${\lim }_{x\to -2^{-}}f\left(x\right)=0,{\lim }_{x\to -2^{+}}f\left(x\right)=0,{\lim }_{x\to -2}f\left(x\right)=0$

Answer: (A)

Verified step by step guidance

1. Observe the graph of the function f(x) around x = -2. Notice the behavior of the function as x approaches -2 from the left (x -> -2^-).
2. As x approaches -2 from the left, the graph of f(x) approaches the y-value of 1. Therefore, lim_{x \(\to\) -2^-} f(x) = 1.
3. Now, observe the behavior of the function as x approaches -2 from the right (x -> -2^+).
4. As x approaches -2 from the right, the graph of f(x) also approaches the y-value of 1. Therefore, lim_{x \(\to\) -2^+} f(x) = 1.
5. Since both one-sided limits as x approaches -2 are equal, the two-sided limit exists and is equal to 1. Therefore, lim_{x \(\to\) -2} f(x) = 1.