Question

Given the domain -2, 2, 4), what is the range for the relation 3x + y = 3?

a) (-9, 3, 9)
b) {0, 5, 7}
c) {9, -3, -9}
d) (-3, 9, 15)

Answer 1

The range for the relation 3x + y = 3 with the domain (-2, 2, 4) is {9, -3, -9}, which matches option c.

Step-by-step explanation:

The question asks to find the range for the relation 3x + y = 3 given the domain (-2, 2, 4). To find the range, we will substitute each value from the domain into the equation and solve for y.

1. For x = -2, the equation becomes 3(-2) + y = 3, which simplifies to -6 + y = 3. Therefore, y = 3 + 6, and y = 9.
2. For x = 2, the equation becomes 3(2) + y = 3, which simplifies to 6 + y = 3. So, y = 3 - 6, and y = -3.
3. For x = 4, the equation becomes 3(4) + y = 3, leading to 12 + y = 3. Hence, y = 3 - 12, and y = -9.

Thus, the range for the relation 3x + y = 3 given the domain (-2, 2, 4) is {9, -3, -9}, which corresponds to option c.