Question

use the graph of the function to determine the indicated limit, if it exists.

\\(\lim_{x \to -4} f(x)\\)

select the correct choice below and fill in any answer boxes in your choice.

a. \\(\lim_{x \to -4} f(x) = \\)

b. the limit does not exist and is neither \\(\infty\\) nor \\(-\infty\\).

Explanation:

Analyze the behavior of the function from the left of \(x = -4\)

$$ \lim_{x \to -4^-} f(x) = \infty $$

Analyze the behavior of the function from the right of \(x = -4\)

$$ \lim_{x \to -4^+} f(x) = \infty $$

Determine the overall limit

$$ \lim_{x \to -4} f(x) = \infty $$

Answer:

• (A) \(\lim_{x \to -4} f(x) = \infty\) (Correct answer)
• (B) The limit does not exist and is neither \(\infty\) nor \(-\infty\).