Given the following function:
[tex]\text{ f(x) = }\sqrt[]{-x\text{ -2}}\text{ + 2}[/tex]y = f(x)
Therefore, let's complete the data table by substituting each x-values to be able to get the respective y-values,
We get,
At x = -2,
[tex]\text{ y = f(x) = }\sqrt[]{-x-2}\text{ + 2}[/tex][tex]\text{f(-2) = }\sqrt[]{-(-2)-2}\text{ + 2}[/tex][tex]\text{ = }\sqrt[]{2\text{ - 2}}\text{ + 2}[/tex][tex]\text{ = }\sqrt[]{0}\text{ + 2}[/tex][tex]\text{ y = f(-2) = 2}[/tex]Therefore, y = 2 at x = -2.
At x = -3,
[tex]\text{ y = f(x) = }\sqrt[]{-x-2}\text{ + 2}[/tex][tex]\text{f(-3) = }\sqrt[]{-(-3)-2}\text{ + 2}[/tex][tex]\text{= }\sqrt[]{3-2}\text{ + 2}[/tex][tex]\text{= }\sqrt[]{1}\text{ + 2}[/tex][tex]\text{= }1\text{ + 2}[/tex][tex]\text{ f(-3) = 3}[/tex]Therefore, y = 3 at x = -3.
At x = -6,