Question

Consider the square root function f(x) = sqrt x + 2 + 1 to complete the table of values below. find each missing value and then graph and connect the points for f(x). x -3, -2, -1 ,2, 7f(x) _ _ _ _ _

Answer 1

Given the function :

`f(x)=\sqrt[]{x+2}+1`

We need to find each missing value

Given x = -3 , -2 , -1 , 2 , 7

So, substitute with each value of x to find the corresponding value of f(x)

`x=-3\rightarrow f(x)=\sqrt[]{-3+2}+1=\sqrt[]{-1}+1`

So, there is no value for f(x) at x = -3 (the function undefined because the square root of -1)

`\begin{gathered} x=-2\rightarrow f(x)=\sqrt[]{-2+2}+1=\sqrt[]{0}+1=0+1=1 \\ \\ x=-1\rightarrow f(x)=\sqrt[]{-1+2}+1=\sqrt[]{1}+1=1+1=2 \\ \\ x=2\rightarrow f(x)=\sqrt[]{2+2}+1=\sqrt[]{4}+1=2+1=3 \\ \\ x=7\rightarrow f(x)=\sqrt[]{7+2}+1=\sqrt[]{9}+1=3+1=4 \end{gathered}`

the graph of the function and the points will be as shown in the following image :