To complete the function table for [tex]\( g(x) = 2x - 5 \)[/tex], we need to substitute each [tex]\( x \)[/tex] value into the function and calculate [tex]\( g(x) \)[/tex].
1. For [tex]\( x = -4 \)[/tex]:
[tex]\[ g(-4) = 2(-4) - 5 \][/tex]
[tex]\[ g(-4) = -8 - 5 \][/tex]
[tex]\[ g(-4) = -13 \][/tex]
2. For [tex]\( x = -2 \)[/tex]:
[tex]\[ g(-2) = 2(-2) - 5 \][/tex]
[tex]\[ g(-2) = -4 - 5 \][/tex]
[tex]\[ g(-2) = -9 \][/tex]
3. For [tex]\( x = 2 \)[/tex]:
[tex]\[ g(2) = 2(2) - 5 \][/tex]
[tex]\[ g(2) = 4 - 5 \][/tex]
[tex]\[ g(2) = -1 \][/tex]
4. For [tex]\( x = 4 \)[/tex]:
[tex]\[ g(4) = 2(4) - 5 \][/tex]
[tex]\[ g(4) = 8 - 5 \][/tex]
[tex]\[ g(4) = 3 \][/tex]
So, the completed function table is:
\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$g(x)$[/tex] \\
\hline
-4 & -13 \\
\hline
-2 & -9 \\
\hline
2 & -1 \\
\hline
4 & 3 \\
\hline
\end{tabular}
