Let's explore the function [tex]\( g(x) = \frac{x-6}{2} \)[/tex] and see how it behaves with different inputs.
1. Plugging in [tex]\( x = 0 \)[/tex]:
[tex]\[
g(0) = \frac{0 - 6}{2} = \frac{-6}{2} = -3
\][/tex]
2. Plugging in [tex]\( x = 6 \)[/tex]:
[tex]\[
g(6) = \frac{6 - 6}{2} = \frac{0}{2} = 0
\][/tex]
3. Plugging in [tex]\( x = 12 \)[/tex]:
[tex]\[
g(12) = \frac{12 - 6}{2} = \frac{6}{2} = 3
\][/tex]
4. Plugging in [tex]\( x = -6 \)[/tex]:
[tex]\[
g(-6) = \frac{-6 - 6}{2} = \frac{-12}{2} = -6
\][/tex]
So, for the given values of [tex]\( x \)[/tex]:
- When [tex]\( x = 0 \)[/tex], [tex]\( g(x) = -3 \)[/tex]
- When [tex]\( x = 6 \)[/tex], [tex]\( g(x) = 0 \)[/tex]
- When [tex]\( x = 12 \)[/tex], [tex]\( g(x) = 3 \)[/tex]
- When [tex]\( x = -6 \)[/tex], [tex]\( g(x) = -6 \)[/tex]
Thus, the results for these inputs are:
[tex]\[
\begin{align*}
g(0) & = -3, \\
g(6) & = 0, \\
g(12) & = 3, \\
g(-6) & = -6.
\end{align*}
\][/tex]
So the results are [tex]\([-3.0, 0.0, 3.0, -6.0]\)[/tex].
