Let's fill in the table step-by-step using the given values.
1. Find [tex]\( x \)[/tex] such that [tex]\( g(x) = 0 \)[/tex]:
Given the function [tex]\( g(x) = 3 - 8x \)[/tex]:
[tex]\[
3 - 8x = 0
\][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[
8x = 3 \implies x = \frac{3}{8} = 0.375
\][/tex]
2. Find [tex]\( g(0) \)[/tex]:
Substituting [tex]\( x = 0 \)[/tex] into the function:
[tex]\[
g(0) = 3 - 8(0) = 3
\][/tex]
3. Find [tex]\( x \)[/tex] such that [tex]\( g(x) = -5 \)[/tex]:
Given the function [tex]\( g(x) = 3 - 8x \)[/tex]:
[tex]\[
3 - 8x = -5
\][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[
-8x = -5 - 3 \implies -8x = -8 \implies x = 1
\][/tex]
4. Find [tex]\( g(3) \)[/tex]:
Substituting [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
g(3) = 3 - 8(3) = 3 - 24 = -21
\][/tex]
Thus, the completed table is:
[tex]\[
\begin{array}{|c|c|}
\hline
x & g(x) \\
\hline
0.375 & 0 \\
\hline
0 & 3 \\
\hline
1 & -5 \\
\hline
3 & -21 \\
\hline
\end{array}
\][/tex]
