Question

Given the domain {-4, 0, 5}, what is the range for the relation 12x + 6y = 24?

Answer 1

Answer:

The range is {12, 4, -6} ⇒ D

Step-by-step explanation:

The range of the relation is the values of y corresponding to the values given for x which is the domain of the relation

∵ The relation is 12x + 6y = 24

∵ The domain of the function is {-4, 0, 5}

→ That means x = -4, 0, 5, we need to find their corresponding values of y

∴ Substitute the values of x in the relation

∵ x = -4

∴ 12(-4) + 6y = 24

∴ -48 + 6y = 24

→ Add 48 to both sides

∴ -48 + 48 + 6y = 24 + 48

∴ 6y = 72

→ Divide both sides by 6 to find y

∴ $\frac{6y}{6}=\frac{72}{6}$

∴ y = 12

∵ x = 0

∴ 12(0) + 6y = 24

∴ 0 + 6y = 24

∴ 6y = 24

→ Divide both sides by 6 to find y

∴ $\frac{6y}{6}=\frac{24}{6}$

∴ y = 4

∵ x = 5

∴ 12(5) + 6y = 24

∴ 60 + 6y = 24

→ Subtract 60 from both sides

∴ 60 - 60 + 6y = 24 - 60

∴ 6y = -36

→ Divide both sides by 6 to find y

∴ $\frac{6y}{6}=\frac{-36}{6}$

∴ y = -6

∵ The range is the values of y which corresponding to the domain

∴ The range is {12, 4, -6}