To fill up the right column, we just need to evaluate the values on the left column on the given function. To evaluate a value on a function, we just substitute the desired value for the variable in the function, and calculate. For the first function and the the first set of values, we have
[tex]\begin{gathered} f(x)=\frac{1}{3}x+7 \\ f(1)=\frac{1}{3}\cdot1+7=\frac{20}{3} \\ f(-6)=\frac{1}{3}\cdot(-6)+7=5 \\ f(7)=\frac{1}{3}\cdot7+7=\frac{28}{3} \\ f(-2)=\frac{1}{3}\cdot(-2)+7=\frac{19}{3} \\ f(3)=\frac{1}{3}\cdot3+7=8 \end{gathered}[/tex]
This means that the values on the right column from top to bottom of the first part are
[tex]\frac{20}{3},5,\frac{28}{3},\frac{19}{3},8[/tex]
Using the same process for the other table, we have
[tex]\begin{gathered} f(x)=4x \\ f(6)=4\cdot6=24 \\ f(2)=4\cdot2=8 \\ f(7)=4\cdot7=28 \\ f(-4)=4\cdot(-4)=-16 \\ f(-9)=4\cdot(-9)=-36 \end{gathered}[/tex]
This means that the values on the right column from top to bottom of the second part are
[tex]24,8,28,-16,-36[/tex]
