Certainly! Let's fill in the table step-by-step:
1. For [tex]\( x = -9 \)[/tex]:
[tex]\[
f(-9) = -5(-9 + 7) = -5(-2) = 10
\][/tex]
So, for [tex]\( x = -9 \)[/tex], [tex]\( f(x) = 10 \)[/tex].
2. We need to find [tex]\( x \)[/tex] such that [tex]\( f(x) = 0 \)[/tex]:
[tex]\[
0 = -5(x + 7) \implies x + 7 = 0 \implies x = -7
\][/tex]
Therefore, for [tex]\( f(x) = 0 \)[/tex], [tex]\( x = -7 \)[/tex].
3. For [tex]\( x = 0 \)[/tex]:
[tex]\[
f(0) = -5(0 + 7) = -5(7) = -35
\][/tex]
So, for [tex]\( x = 0 \)[/tex], [tex]\( f(x) = -35 \)[/tex].
4. We need to find [tex]\( x \)[/tex] such that [tex]\( f(x) = -60 \)[/tex]:
[tex]\[
-60 = -5(x + 7) \implies x + 7 = 12 \implies x = 5
\][/tex]
Therefore, when [tex]\( f(x) = -60 \)[/tex], [tex]\( x = 5 \)[/tex].
Now, we can complete the table:
[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $f(x)$ \\
\hline
-9 & 10 \\
\hline
-7 & 0 \\
\hline
0 & -35 \\
\hline
5 & -60 \\
\hline
\end{tabular}
\][/tex]
