Let's evaluate the piecewise function [tex]\( g(x) \)[/tex] at the specified values.
The function [tex]\( g(x) \)[/tex] is defined as follows:
[tex]\[
g(x) = \begin{cases}
x + 4, & \text{if } -5 \leq x \leq -1 \\
2 - x, & \text{if } -1 < x \leq 5
\end{cases}
\][/tex]
### Evaluating [tex]\( g(-4) \)[/tex]:
For [tex]\( x = -4 \)[/tex]:
[tex]\[
-5 \leq -4 \leq -1 \quad \text{(so we use the first piece of the function)}
\][/tex]
[tex]\[
g(-4) = -4 + 4 = 0
\][/tex]
### Evaluating [tex]\( g(-2) \)[/tex]:
For [tex]\( x = -2 \)[/tex]:
[tex]\[
-5 \leq -2 \leq -1 \quad \text{(so we use the first piece of the function)}
\][/tex]
[tex]\[
g(-2) = -2 + 4 = 2
\][/tex]
### Evaluating [tex]\( g(0) \)[/tex]:
For [tex]\( x = 0 \)[/tex]:
[tex]\[
-1 < 0 \leq 5 \quad \text{(so we use the second piece of the function)}
\][/tex]
[tex]\[
g(0) = 2 - 0 = 2
\][/tex]
### Evaluating [tex]\( g(3) \)[/tex]:
For [tex]\( x = 3 \)[/tex]:
[tex]\[
-1 < 3 \leq 5 \quad \text{(so we use the second piece of the function)}
\][/tex]
[tex]\[
g(3) = 2 - 3 = -1
\][/tex]
### Evaluating [tex]\( g(4) \)[/tex]:
For [tex]\( x = 4 \)[/tex]:
[tex]\[
-1 < 4 \leq 5 \quad \text{(so we use the second piece of the function)}
\][/tex]
[tex]\[
g(4) = 2 - 4 = -2
\][/tex]
Thus, the evaluated values are:
[tex]\[
\begin{array}{l}
g(-4) = 0 \\
g(-2) = 2 \\
g(0) = 2 \\
g(3) = -1 \\
g(4) = -2
\end{array}
\][/tex]
