Question

find the limit.
\lim\limits_{x\to -2} (9x + 8)

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

\bigcirc a. \lim\limits_{x\to -2} (9x + 8) = \square (simplify your answer.)
\bigcirc b. the limit does not exist.

Explanation:

Step1: Recall the limit rule for linear functions

For a linear function \( f(x) = ax + b \), the limit as \( x \to c \) is \( f(c) \), because linear functions are continuous everywhere. So we can directly substitute \( x = -2 \) into the function \( 9x + 8 \).

Step2: Substitute \( x = -2 \) into the function

Substitute \( x = -2 \) into \( 9x + 8 \):
\( 9(-2) + 8 \)
First, calculate \( 9(-2) = -18 \). Then, add 8: \( -18 + 8 = -10 \).

Answer:

A. \( \lim\limits_{x \to -2} (9x + 8) = -10 \)