To complete the table for the function [tex]\( g(x) = 3 - 8x \)[/tex], we need to find the corresponding inputs and outputs. Here's how we do it step-by-step:
1. Find [tex]\( x \)[/tex] such that [tex]\( g(x) = 0 \)[/tex]:
[tex]\[
g(x) = 0 \implies 3 - 8x = 0 \implies 8x = 3 \implies x = \frac{3}{8}
\][/tex]
So, for [tex]\( g(x) = 0 \)[/tex], [tex]\( x \)[/tex] is:
[tex]\[
\boxed{\frac{3}{8}}
\][/tex]
2. Find [tex]\( g(0) \)[/tex]:
[tex]\[
g(0) = 3 - 8 \cdot 0 = 3
\][/tex]
So, for [tex]\( x = 0 \)[/tex], [tex]\( g(x) \)[/tex] is:
[tex]\[
\boxed{3}
\][/tex]
3. Find [tex]\( x \)[/tex] such that [tex]\( g(x) = -5 \)[/tex]:
[tex]\[
g(x) = -5 \implies 3 - 8x = -5 \implies 8x = 8 \implies x = 1
\][/tex]
So, for [tex]\( g(x) = -5 \)[/tex], [tex]\( x \)[/tex] is:
[tex]\[
\boxed{1}
\][/tex]
4. Find [tex]\( g(3) \)[/tex]:
[tex]\[
g(3) = 3 - 8 \cdot 3 = 3 - 24 = -21
\][/tex]
So, for [tex]\( x = 3 \)[/tex], [tex]\( g(x) \)[/tex] is:
[tex]\[
\boxed{-21}
\][/tex]
Now, we can complete the table:
[tex]\[
\begin{tabular}{|c|c|}
\hline x & g(x) \\
\hline \boxed{\frac{3}{8}} & 0 \\
\hline 0 & \boxed{3} \\
\hline \boxed{1} & -5 \\
\hline 3 & \boxed{-21} \\
\hline
\end{tabular}
\][/tex]
