Question

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

A.
{-12, -4, 6}
B.
{-4, 4, 14}
C.
{12, 4, -6}
D.
{2, 4, 9}

Answer 1

To determine the range for the relation defined by the equation \(12x + 6y = 24\) given the domain \(\{-4, 0, 5\}\), we need to solve for \(y\) in terms of \(x\):

1. Rearranging the equation:
\[
6y = 24 - 12x
\]
\[
y = 4 - 2x
\]

Now, we will compute the value of \(y\) for each value of \(x\) in the given domain.

- For \(x = -4\):
\[
y = 4 - 2(-4) = 4 + 8 = 12
\]

- For \(x = 0\):
\[
y = 4 - 2(0) = 4
\]

- For \(x = 5\):
\[
y = 4 - 2(5) = 4 - 10 = -6
\]

Now we compile the outputs for each input:
- When \(x = -4\), \(y = 12\)
- When \(x = 0\), \(y = 4\)
- When \(x = 5\), \(y = -6\)

Thus, the range of the relation is:
\[
\{12, 4, -6\}
\]

From the options given:
C. \{12, 4, -6\} is the correct answer.