To determine the value of the function [tex]\( f(x) \)[/tex] at [tex]\( x = -8 \)[/tex] for the given piecewise function:
[tex]\[
f(x)=\begin{array}{rr}
9 x+1, & \text { for } x<8 \\
8 x, & \text { for } 8 \leq x \leq 10 \\
8-9 x, & \text { for } x>10
\end{array}
\][/tex]
we need to find which piece of the piecewise function is applicable for [tex]\( x = -8 \)[/tex].
Since [tex]\( -8 \)[/tex] is less than [tex]\( 8 \)[/tex], we use the first piece of the function:
[tex]\[
f(x) = 9x + 1 \quad \text{for} \quad x < 8
\][/tex]
Now, substitute [tex]\( x = -8 \)[/tex] into this equation:
[tex]\[
f(-8) = 9(-8) + 1
\][/tex]
Calculate the expression step-by-step:
[tex]\[
9(-8) = -72
\][/tex]
Then,
[tex]\[
-72 + 1 = -71
\][/tex]
Thus, the value of [tex]\( f(-8) \)[/tex] is [tex]\(-71\)[/tex].
So, the correct answer is:
A. [tex]\(-71\)[/tex]
