Let's analyze the piecewise function [tex]\( g(x) \)[/tex] for the given values of [tex]\( x \)[/tex].
The function is defined as:
[tex]\[
g(x) = \begin{cases}
6 & \text{if } -8 \leq x < -2 \\
0 & \text{if } -2 \leq x < 4 \\
-4 & \text{if } 4 \leq x < 10
\end{cases}
\][/tex]
### Step-by-Step Solution:
1. Finding [tex]\( g(-2) \)[/tex]:
- [tex]\( -2 \)[/tex] falls into the interval [tex]\( -2 \leq x < 4 \)[/tex].
- According to the piecewise function definition, [tex]\( g(x) = 0 \)[/tex] for [tex]\( -2 \leq x < 4 \)[/tex].
Therefore, [tex]\( g(-2) = 0 \)[/tex].
2. Finding [tex]\( g(4) \)[/tex]:
- [tex]\( 4 \)[/tex] falls into the interval [tex]\( 4 \leq x < 10 \)[/tex].
- According to the piecewise function definition, [tex]\( g(x) = -4 \)[/tex] for [tex]\( 4 \leq x < 10 \)[/tex].
Therefore, [tex]\( g(4) = -4 \)[/tex].
### Final Values:
[tex]\[
g(-2) = 0
\][/tex]
[tex]\[
g(4) = -4
\][/tex]
So, the values of the function at [tex]\( x = -2 \)[/tex] and [tex]\( x = 4 \)[/tex] are:
[tex]\[
g(-2) = 0
\][/tex]
[tex]\[
g(4) = -4
\][/tex]
