Question

The domain of this function is (-12,-6, 3, 15) y=-2/3x+7Complete the table based on the given domain.

Answer 1

Step-by-step explanation:

The domain represents the possible x-values

The range represents the possible y-values

From what is given in the question, we have a set of possible x-values

To get the corresponding y-values, we have to substitute the x-values in the given functions

We proceed as follows:

a) x = -6

`\begin{gathered} y\text{ = -}(2)/(3)x\text{ + 7} \\ \\ y\text{ = -}(2)/(3)(-6)\text{ + 7} \\ \\ y\text{ = 4 + 7 = 11} \end{gathered}`

b) y = 5

`\begin{gathered} 5\text{ = -}(2)/(3)x\text{ + 7} \\ \\ multiply\text{ through by 3} \\ 15\text{ = -2x + 21} \\ 2x\text{ = 21-15} \\ 2x\text{ = 6} \\ x\text{ = }(6)/(2) \\ x\text{ = 3} \end{gathered}`

c) x = 15

`\begin{gathered} y\text{ = -}(2)/(3)*15\text{ + 7} \\ \\ y\text{ = -10 + 7 = -3} \end{gathered}`

d) y = 15

`\begin{gathered} 15\text{ = -}(2)/(3)x\text{ + 7} \\ \\ multiply\text{ through by 3} \\ 45\text{ = -2x + 21} \\ 2x\text{ = 21-45} \\ 2x\text{ = -24} \\ x\text{ = -}(24)/(2) \\ x\text{ = -12} \end{gathered}`