review the graph of function f(x). for which value of c does lim f(x) not exist? x→c -4 -2 2 4

Answer:

C. 2

Explanation:

Step1: Recall limit - existence condition

The limit $\lim_{x\rightarrow c}f(x)$ exists if $\lim_{x\rightarrow c^{-}}f(x)=\lim_{x\rightarrow c^{+}}f(x)$.

Step2: Analyze $x = - 4$

As $x\rightarrow - 4$, the left - hand limit and right - hand limit are equal. The function approaches the same value from both sides.

Step3: Analyze $x=-2$

As $x\rightarrow - 2$, the left - hand limit and right - hand limit are equal. The function approaches the same value from both sides.

Step4: Analyze $x = 2$

As $x\rightarrow2^{-}$, the function approaches a value on the orange - line segment. As $x\rightarrow2^{+}$, the function approaches a different value (the value of the isolated point). So, $\lim_{x\rightarrow2^{-}}f(x)\neq\lim_{x\rightarrow2^{+}}f(x)$, and $\lim_{x\rightarrow2}f(x)$ does not exist.

Step5: Analyze $x = 4$

As $x\rightarrow4$, the left - hand limit and right - hand limit are equal. The function approaches the same value from both sides.