Question

select the correct answer. given the domain {-4, 0, 5}, what is the range for the relation 12x + 6y = 24? a. {-12, -4, 8} b. {2, 4, 9} c. {-4, 4, 14} d. {12, 4, -6}

Explanation:

Step1: Solve for y in the equation

First, we start with the equation \(12x + 6y = 24\). We can simplify this equation by dividing every term by 6: \(2x + y = 4\), then solve for \(y\): \(y = 4 - 2x\).

Step2: Substitute each x from the domain

The domain is \(\{-4, 0, 5\}\). We substitute each value of \(x\) into the equation for \(y\):

• For \(x = -4\): \(y = 4 - 2(-4) = 4 + 8 = 12\)
• For \(x = 0\): \(y = 4 - 2(0) = 4\)
• For \(x = 5\): \(y = 4 - 2(5) = 4 - 10 = -6\)

Step3: Determine the range

The range is the set of all resulting \(y\)-values, so the range is \(\{12, 4, -6\}\).

Answer:

D. {12, 4, -6}