To solve for [tex]\( g(x) \)[/tex] given [tex]\( g(x) = -3x^2 \)[/tex] and [tex]\( x \)[/tex] values of [tex]\(-3, -2, -1, 0, 1, 2, 3\)[/tex], we will evaluate [tex]\( g(x) \)[/tex] for each of these [tex]\( x \)[/tex] values step by step.
1. When [tex]\( x = -3 \)[/tex]:
[tex]\[
g(-3) = -3 \cdot (-3)^2 = -3 \cdot 9 = -27
\][/tex]
2. When [tex]\( x = -2 \)[/tex]:
[tex]\[
g(-2) = -3 \cdot (-2)^2 = -3 \cdot 4 = -12
\][/tex]
3. When [tex]\( x = -1 \)[/tex]:
[tex]\[
g(-1) = -3 \cdot (-1)^2 = -3 \cdot 1 = -3
\][/tex]
4. When [tex]\( x = 0 \)[/tex]:
[tex]\[
g(0) = -3 \cdot 0^2 = -3 \cdot 0 = 0
\][/tex]
5. When [tex]\( x = 1 \)[/tex]:
[tex]\[
g(1) = -3 \cdot 1^2 = -3 \cdot 1 = -3
\][/tex]
6. When [tex]\( x = 2 \)[/tex]:
[tex]\[
g(2) = -3 \cdot 2^2 = -3 \cdot 4 = -12
\][/tex]
7. When [tex]\( x = 3 \)[/tex]:
[tex]\[
g(3) = -3 \cdot 3^2 = -3 \cdot 9 = -27
\][/tex]
Given these calculations, the corresponding [tex]\( g(x) \)[/tex] values for the provided [tex]\( x \)[/tex] values are:
[tex]\[
\begin{array}{cc}
x & g(x) \\
\hline
-3 & -27 \\
-2 & -12 \\
-1 & -3 \\
0 & 0 \\
1 & -3 \\
2 & -12 \\
3 & -27 \\
\end{array}
\][/tex]
Thus, the resulting array [tex]\( g(x) \)[/tex] for [tex]\( x = [-3, -2, -1, 0, 1, 2, 3] \)[/tex] is:
[tex]\[
[-27, -12, -3, 0, -3, -12, -27]
\][/tex]
