Question

See attachment for question (I will report you if you are only doing it for the points)

Answer 1

x => y

-6 => 9

3 => 5

15 => -3

-12 => 15

Explanation:

Given the domain function, {-12, -6, 3, 15}, and the equation of the function,
`y = -(2)/(3)x + 7`, we can complete the given table by simply plugging in the value of either x to find y, or y to find x in the table given. The domain values are all x-values you have in the table.

Find y when x = -6:

`y = -(2)/(3)(-6) + 7`

`y = -(2)/(1)(-2) + 7`

`y = 2 + 7`

`y = 9`

Find x when y = 5:

`5 = -(2)/(3)x + 7`

`5 - 7 = -(2)/(3)x + 7 - 7`

`-2 = -(2)/(3)x`

`-2 = (-2x)/(3)`

`-2*3 = (-2x)/(3)*3`

`-6 = -2x`

`(-6)/(-2) = (-2x)/(-2)`

`3 = x`

`x = 3`

Find y when x = 15:

`y = -(2)/(3)(15) + 7`

`y = -(2)/(1)(5) + 7`

`y = -10 + 7`

`y = -3`

Find x when y = 15:

`15 = -(2)/(3)x + 7`

`15 - 7 = -(2)/(3)x + 7 - 7`

`8 = -(2)/(3)x`

`8 = (-2x)/(3)`

`8*3 = (-2x)/(3)*3`

`24 = -2x`

`(24)/(-2) = (-2x)/(-2)`

`-12 = x`

`x = -12`