Question

question 2
for what value(s) of x does the limit of f(x) does not exist?
-4 & 2
-4, 2 & 4
-4, 12 & 4
-4

Explanation:

Step1: Recall limit - existence condition

The limit of a function $f(x)$ as $x$ approaches $a$ exists if and only if $\lim_{x
ightarrow a^{-}}f(x)=\lim_{x
ightarrow a^{+}}f(x)$.

Step2: Analyze the graph at $x = - 4$

As $x$ approaches $-4$ from the left and the right, the function values do not approach the same value. There is a jump - like behavior at $x=-4$.

Step3: Analyze the graph at $x = 2$

As $x$ approaches $2$ from the left and the right, the function values do not approach the same value. There is a break in the graph at $x = 2$.

Step4: Analyze the graph at $x = 4$

As $x$ approaches $4$ from the left and the right, the function values do not approach the same value. There is a hole - like or break - like behavior at $x = 4$.

Answer:

$-4,2,4$