SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given function.
[tex]f(x)=-5(x+7)[/tex]
STEP 2: Complete the table
When x=-9
[tex]\begin{gathered} f(x)=-5(x+7) \\ \text{when x=}-9,\text{ we substitute -9 for x in the function} \\ f(-9)=-5(-9+7)=-5(-2)=-5\times-2=10 \end{gathered}[/tex]
STEP 3: Calculate for x when f(x)=0
[tex]\begin{gathered} f(x)=-5(x+7) \\ \text{when f(x)=}0,\text{ we substitute 0 for f(x) in the function} \\ 0=-5(x+7) \\ By\text{ expansion,} \\ 0=-5x-35 \\ \text{Add 5x to both sides} \\ 0+5x=-5x-35+5x \\ 5x=-35 \\ \text{Divide both sides by 5} \\ \frac{5x}{5}=\frac{-35}{5} \\ x=-7 \end{gathered}[/tex]
STEP 4: Calculate for f(x) when x=0
[tex]\begin{gathered} f(x)=-5(x+7) \\ \text{when x=}0,\text{ we substitute 0 for x in the function} \\ f(0)=-5(0+7)=-5(7)=-35 \end{gathered}[/tex]
STEP 5: Calculate for x when f(x)=-60
[tex]\begin{gathered} f(x)=-5(x+7) \\ \text{when f(x)=-6}0,\text{ we substitute -60 for f(x) in the function} \\ -60=-5(x+7) \\ By\text{ expansion,} \\ -60=-5x-35 \\ \text{Add 5x to both sides} \\ -60+5x=-5x-35+5x \\ -60+5x=-35 \\ \text{Add 60 to both sides} \\ -60+5x+60=-35+60 \\ 5x=25 \\ \text{Divide both sides by 5} \\ \frac{5x}{5}=\frac{25}{5} \\ x=5 \end{gathered}[/tex]
Hence, the completed table will be:
