Use the graph of $f\left(x\right)$ to estimate the value of the limit or state that it does not exist (DNE).
$\lim_{x\rarr-2}f\left(x\right)$

• A. $-3$
• B. $1$
• C. $4$
• D. $DNE$

Answer: (D)

Verified step by step guidance

1. To estimate the limit \( \lim_{x \to -2} f(x) \), we need to observe the behavior of the function \( f(x) \) as \( x \) approaches \( -2 \) from both the left and the right.
2. Examine the graph to see if the function approaches a specific value as \( x \) approaches \( -2 \). Look for continuity or any jumps, holes, or asymptotes at \( x = -2 \).
3. From the graph, observe that as \( x \) approaches \( -2 \) from the left, the function appears to be moving towards a certain value. Similarly, check the behavior as \( x \) approaches \( -2 \) from the right.
4. Notice that the graph shows a jump discontinuity at \( x = -2 \), meaning the left-hand limit and the right-hand limit do not match.
5. Since the left-hand limit and the right-hand limit are not equal, the limit \( \lim_{x \to -2} f(x) \) does not exist (DNE).