Question

Complete the function table for the given domain, and plot the points on the graph. 1(x) = (x - 5)² + 1 I 2 3 4 5 6 Drawing Tools Click on a tool to begin drawing. 3 Delete Undo Reset Select Point f(x) 10 8 6 4 A N -10 -8 -6 -4 -2 2 4 6 8 10 -2 -6 -8

Answer 1

To solve the exercise and complete the table, first replace the values of x given in the equation and in this way obtain their corresponding y values.

So, you have

$\begin{gathered} x=2 \\ f(x)=(x-5)^2+1 \\ f(1)=(2-5)^2+1 \\ f(1)=(-3)^2+1 \\ f(1)=9+1 \\ f(1)=10 \\ \text{ Then, you have the coordinate pair} \\ (2,10) \end{gathered}$

$\begin{gathered} x=3 \\ f(x)=(x-5)^2+1 \\ f(3)=(3-5)^2+1 \\ f(3)=(-2)^2+1 \\ f(3)=4+1 \\ f(3)=5 \\ \text{ Then, you have the coordinate pair} \\ (3,5) \end{gathered}$

$\begin{gathered} x=4 \\ f(x)=(x-5)^2+1 \\ f(4)=(4-5)^2+1 \\ f(4)=(-1)^2+1 \\ f(4)=1+1 \\ f(4)=2 \\ \text{ Then, you have the coordinate pair} \\ (4,2) \end{gathered}$

$\begin{gathered} x=5 \\ f(x)=(x-5)^2+1 \\ f(5)=(5-5)^2+1 \\ f(5)=(0)^2+1 \\ f(5)=0+1 \\ f(5)=1 \\ \text{ Then, you have the coordinate pair} \\ (5,1) \end{gathered}$

$\begin{gathered} x=6 \\ f(x)=(x-5)^2+1 \\ f(6)=(6-5)^2+1 \\ f(6)=(1)^2+1 \\ f(6)=1+1 \\ f(6)=2 \\ \text{ Then, you have the coordinate pair} \\ (6,2) \end{gathered}$

So, the table function looks like this

Finally, plotting the points on the graph, you have