Suppose that
\[
3(x+4)-2 \leq g(x) \leq(x+4)^{3}
\]
for all $x$ in the interval $(-4,-2)$.
Find $\lim _{x \rightarrow-3} g(x)$.
If the limit does not exist, click on "Does Not Exist."

Step 1 ：We are given that the function g(x) is bounded by two functions, 3(x+4)-2 and (x+4)^3, for all x in the interval (-4,-2).

Step 2 ：We are asked to find the limit of g(x) as x approaches -3. Since -3 is within the interval (-4,-2), we can use the Squeeze Theorem.

Step 3 ：The Squeeze Theorem states that if a function h(x) is always between two other functions f(x) and g(x) (i.e., f(x) ≤ h(x) ≤ g(x)) and the limits of f(x) and g(x) as x approaches a certain value are the same, then the limit of h(x) as x approaches that value is also the same.

Step 4 ：Therefore, we need to find the limits of 3(x+4)-2 and (x+4)^3 as x approaches -3.

Step 5 ：The limits of both bounding functions as x approaches -3 are the same (1).

Step 6 ：Therefore, by the Squeeze Theorem, the limit of g(x) as x approaches -3 is also 1.

Step 7 ：Final Answer: The limit of g(x) as x approaches -3 is \(\boxed{1}\).