Question

If y − 1 = 4x, which of the following sets represents possible inputs and outputs of the function, represented as ordered pairs?

a. {(1, 4), (2, 8), (3, 12)}
b. {(4, 1), (8, 2), (12, 3)}
c. {(0, 1), (1, 5), (2, 9)}
d. {(1, 0), (5, 1), (9, 2)}

Answer 1

The set {(0, 1), (1, 5), (2, 9)} represents possible inputs and outputs of the function y - 1 = 4x.

Step-by-step explanation:

The given equation is y - 1 = 4x.

To determine the possible inputs and outputs in the form of ordered pairs, we need to rearrange the equation to isolate y.

Adding 1 to both sides of the equation, we get y = 4x + 1.

Now, we can substitute different values of x to find the corresponding values of y.

Let's check the sets:

(a) Substituting x = 1 gives y = 4(1) + 1 = 5. This matches with the ordered pair (1, 5).

(b) Substituting x = 4 gives y = 4(4) + 1 = 17. This does not match with any ordered pair.

(c) Substituting x = 2 gives y = 4(2) + 1 = 9. This matches with the ordered pair (2, 9).

(d) Substituting x = 5 gives y = 4(5) + 1 = 21. This does not match with any ordered pair.

Therefore, the only set that represents possible inputs and outputs of the function as ordered pairs is option c. {(0, 1), (1, 5), (2, 9)}.