Sure! Let's complete the function table step-by-step using the given function [tex]\( f(x) = 2x - 2 \)[/tex].
1. For [tex]\( x = -5 \)[/tex]:
[tex]\[
f(-5) = 2(-5) - 2 = -10 - 2 = -12
\][/tex]
So, [tex]\( f(-5) = -12 \)[/tex].
2. For [tex]\( x = -4 \)[/tex]:
[tex]\[
f(-4) = 2(-4) - 2 = -8 - 2 = -10
\][/tex]
So, [tex]\( f(-4) = -10 \)[/tex].
3. For [tex]\( x = 1 \)[/tex]:
[tex]\[
f(1) = 2(1) - 2 = 2 - 2 = 0
\][/tex]
So, [tex]\( f(1) = 0 \)[/tex].
4. For [tex]\( x = 3 \)[/tex]:
[tex]\[
f(3) = 2(3) - 2 = 6 - 2 = 4
\][/tex]
So, [tex]\( f(3) = 4 \)[/tex].
5. For [tex]\( x = 5 \)[/tex]:
[tex]\[
f(5) = 2(5) - 2 = 10 - 2 = 8
\][/tex]
So, [tex]\( f(5) = 8 \)[/tex].
Now, let's complete the function table with these values:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $f(x)$ \\
\hline
-5 & -12 \\
\hline
-4 & -10 \\
\hline
1 & 0 \\
\hline
3 & 4 \\
\hline
5 & 8 \\
\hline
\end{tabular}
\][/tex]
