Question

Type the correct answer in each box. Use numerals instead of words.

The domain of this function is {-12, -6, 3, 15}.



Complete the table based on the given domain.

Answer 1

At x = –6, y = 11

At x = 3, y = 5

At x = 15, y = –3

At x = –12, y = 15

Solution:

The function is
`y=-(2)/(3) x+7`.

The domain of the function is {–12, –6, 3, 15}.

Substitute x = –6 in the function to find y.

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

y = 4 + 7

y = 11

Substitute y = 5 in the function to find x.

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

Subtract 7 from both sides, we get

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

Multiply by
`-(3)/(2)` on both sides, we get

x = 3

Substitute x = 15 in the function to find y.

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

y = –10 + 7

y = –3

Substitute y = 15 in the function to find x.

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

Subtract 7 from both sides, we get

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

Multiply by
`-(3)/(2)` on both sides, we get

x = –12

At x = –6, y = 11

At x = 3, y = 5

At x = 15, y = –3

At x = –12, y = 15