Certainly! Let's complete the table for the function [tex]\( g(x) = 3 - 8x \)[/tex].
1. First, we need to find the value of [tex]\( x \)[/tex] when [tex]\( g(x) = 0 \)[/tex]:
[tex]\[ 0 = 3 - 8x \][/tex]
From previous calculations, when [tex]\( g(x) = 0 \)[/tex], [tex]\( x = 0.375 \)[/tex].
2. Next, we need to find the value of [tex]\( g(x) \)[/tex] when [tex]\( x = 0 \)[/tex]:
[tex]\[ g(0) = 3 - 8 \cdot 0 = 3 \][/tex]
From previous calculations, [tex]\( g(0) = 3 \)[/tex].
3. Next, we need to find the value of [tex]\( x \)[/tex] when [tex]\( g(x) = -5 \)[/tex]:
[tex]\[ -5 = 3 - 8x \][/tex]
From previous calculations, when [tex]\( g(x) = -5 \)[/tex], [tex]\( x = 1.0 \)[/tex].
4. Finally, we need to find the value of [tex]\( g(x) \)[/tex] when [tex]\( x = 3 \)[/tex]:
[tex]\[ g(3) = 3 - 8 \cdot 3 = -21 \][/tex]
From previous calculations, [tex]\( g(3) = -21 \)[/tex].
Now, we can complete the table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $g(x)$ \\
\hline
0.375 & 0 \\
\hline
0 & 3 \\
\hline
1.0 & -5 \\
\hline
3 & -21 \\
\hline
\end{tabular}
\][/tex]
