Certainly! Let's complete the table for the given function rule [tex]\( y = -x - 9 \)[/tex]. We'll determine the values of [tex]\( y \)[/tex] corresponding to each given [tex]\( x \)[/tex] value.
Given [tex]\( x \)[/tex] values are: [tex]\( -2, -1, 0, 1, 2 \)[/tex].
1. For [tex]\( x = -2 \)[/tex]:
[tex]\[
y = -(-2) - 9 = 2 - 9 = -7
\][/tex]
So, [tex]\( y = -7 \)[/tex].
2. For [tex]\( x = -1 \)[/tex]:
[tex]\[
y = -(-1) - 9 = 1 - 9 = -8
\][/tex]
So, [tex]\( y = -8 \)[/tex].
3. For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = -(0) - 9 = 0 - 9 = -9
\][/tex]
So, [tex]\( y = -9 \)[/tex].
4. For [tex]\( x = 1 \)[/tex]:
[tex]\[
y = -(1) - 9 = -1 - 9 = -10
\][/tex]
So, [tex]\( y = -10 \)[/tex].
5. For [tex]\( x = 2 \)[/tex]:
[tex]\[
y = -(2) - 9 = -2 - 9 = -11
\][/tex]
So, [tex]\( y = -11 \)[/tex].
Now, we can complete the table:
[tex]\[
\begin{array}{l|lllll}
\text{x} & -2 & -1 & 0 & 1 & 2 \\
\hline
\text{y} & -7 & -8 & -9 & -10 & -11 \\
\end{array}
\][/tex]
