Question

Complete the data table for the function f(x) = -x - 2 + 2.

Answer 1

Given the following function:

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

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,

`\text{ y = f(x) = }\sqrt[]{-x-2}\text{ + 2}`
`\text{f(-2) = }\sqrt[]{-(-2)-2}\text{ + 2}`
`\text{ = }\sqrt[]{2\text{ - 2}}\text{ + 2}`
`\text{ = }\sqrt[]{0}\text{ + 2}`
`\text{ y = f(-2) = 2}`

Therefore, y = 2 at x = -2.

At x = -3,

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

Therefore, y = 3 at x = -3.

At x = -6,