To find the range for the given relation, we need to solve the equation for y and substitute the values of x from the domain set to get the corresponding y-values.
Equation: 12x + 6y = 24
Let's substitute the first value from the domain set, x = -4:
12(-4) + 6y = 24
-48 + 6y = 24
6y = 72
y = 12
We substitute x = -4 and get y = 12. Therefore, (-4, 12) is a point on the graph of the relation.
Let's substitute the second value from the domain set, x = 0:
12(0) + 6y = 24
0 + 6y = 24
6y = 24
y = 4
We substitute x = 0 and get y = 4. Therefore, (0, 4) is a point on the graph of the relation.
Finally, let's substitute the third value from the domain set, x = 5:
12(5) + 6y = 24
60 + 6y = 24
6y = -36
y = -6
We substitute x = 5 and get y = -6. Therefore, (5, -6) is a point on the graph of the relation.
The range of the relation is the set of y-values from the points we obtained: {12, 4, -6}.
Therefore, the correct answer is D. {12, 4, -6}.
Given the domain {-4, 0, 5}, what is the range for the relation 12x + 6y = 24?
A.
{-4, 4, 14}
B.
{-12, -4, 6}
C.
{2, 4, 9}
D.
{12, 4, -6}
1 answer
1 answer