Answer:
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
[tex]\begin{gathered} y\text{ = -}\frac{2}{3}x\text{ + 7} \\ \\ y\text{ = -}\frac{2}{3}(-6)\text{ + 7} \\ \\ y\text{ = 4 + 7 = 11} \end{gathered}[/tex]
b) y = 5
[tex]\begin{gathered} 5\text{ = -}\frac{2}{3}x\text{ + 7} \\ \\ multiply\text{ through by 3} \\ 15\text{ = -2x + 21} \\ 2x\text{ = 21-15} \\ 2x\text{ = 6} \\ x\text{ = }\frac{6}{2} \\ x\text{ = 3} \end{gathered}[/tex]
c) x = 15
[tex]\begin{gathered} y\text{ = -}\frac{2}{3}\times15\text{ + 7} \\ \\ y\text{ = -10 + 7 = -3} \end{gathered}[/tex]
d) y = 15
[tex]\begin{gathered} 15\text{ = -}\frac{2}{3}x\text{ + 7} \\ \\ multiply\text{ through by 3} \\ 45\text{ = -2x + 21} \\ 2x\text{ = 21-45} \\ 2x\text{ = -24} \\ x\text{ = -}\frac{24}{2} \\ x\text{ = -12} \end{gathered}[/tex]
