Question

Which set of ordered pairs represents y as a function of x?

A) F {(2, 5), (3, 1), (2, 1), (4, 7)}
B) G ((3, 2), (4, 3), (5, 2), (2, 6)}
C) H {(1, 3), (3, 5), (2, 5). (1, 6)}
D) J {(4, 7), (4, 6), (4, 4), (4, 1)}

Answer 1

The set that represents y as a function of x is Set G: {(3, 2), (4, 3), (5, 2), (2, 6)}, as it adheres to the definition of a function with each x-value corresponding to exactly one y-value.

Step-by-step explanation:

To determine which set of ordered pairs represents y as a function of x, we need to ensure that for every value of x there is exactly one corresponding value of y. In other words, an x-value cannot be paired with more than one y-value.

• Set F: {(2, 5), (3, 1), (2, 1), (4, 7)} has the x-value 2 paired with two different y-values (5 and 1). This violates the definition of a function.
• Set G: {(3, 2), (4, 3), (5, 2), (2, 6)} does not have any repeated x-values. Each x-value is associated with one and only one y-value.
• Set H: {(1, 3), (3, 5), (2, 5), (1, 6)} has the x-value 1 paired with two different y-values (3 and 6), which is not allowed for a function.
• Set J: {(4, 7), (4, 6), (4, 4), (4, 1)} has the x-value 4 paired with multiple y-values, which also violates the definition of a function.

Therefore, the set that represents y as a function of x is Set G: {(3, 2), (4, 3), (5, 2), (2, 6)}.