To solve this problem, let's determine the corresponding [tex]\( y \)[/tex] values for the given [tex]\( x \)[/tex] values using the function [tex]\( h(x) = 4(x - 2) \)[/tex].
### Step-by-Step Solution:
1. Given Function:
[tex]\[
h(x) = 4(x - 2)
\][/tex]
2. Determine [tex]\( y \)[/tex] when [tex]\( x = -2 \)[/tex]:
[tex]\[
h(-2) = 4(-2 - 2)
= 4(-4)
= -16
\][/tex]
So, when [tex]\( x = -2 \)[/tex], [tex]\( y = -16 \)[/tex].
3. Determine [tex]\( y \)[/tex] when [tex]\( x = -1 \)[/tex]:
[tex]\[
h(-1) = 4(-1 - 2)
= 4(-3)
= -12
\][/tex]
So, when [tex]\( x = -1 \)[/tex], [tex]\( y = -12 \)[/tex].
4. Determine [tex]\( y \)[/tex] when [tex]\( x = 1 \)[/tex]:
[tex]\[
h(1) = 4(1 - 2)
= 4(-1)
= -4
\][/tex]
So, when [tex]\( x = 1 \)[/tex], [tex]\( y = -4 \)[/tex].
### Filling in the Table:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
\multicolumn{4}{|c|}{ $h(x) = 4(x-2)$ } \\
\hline
$x$ & -2 & -1 & 1 \\
\hline
$y$ & -16 & -12 & -4 \\
\hline
\end{tabular}
\][/tex]
In summary, the corresponding [tex]\( y \)[/tex] values for [tex]\( x = -2, -1, 1 \)[/tex] are [tex]\( -16, -12, -4 \)[/tex] respectively.
