Question

Which set of ordered pairs represents a function?

A) {(9, -7), (1, -3), (6, 7), (6, -6)
B) {(-7, 7), (5, 3), (-7, -7), (1, -9)
C) {(8, -6), (-9, 2), (-9, -8), (-3, 4)
D) {(-5, -5), (-9, 0), (-8, 5), (-6, 5)

Answer 1

Option D, which contains the set of ordered pairs {(-5, -5), (-9, 0), (-8, 5), (-6, 5)}, represents a function as each input has exactly one corresponding output.

Step-by-step explanation:

The question asks which set of ordered pairs represents a function. To determine if a set of ordered pairs represents a function, we must check if each input, or x-value, is associated with exactly one output, or y-value. This is based on the definition of a function in mathematics.

Reviewing the options given:

• Option A) has two pairs with the same first element (6, 7) and (6, -6), which means this does not represent a function.
• Option B) has two pairs with the same first element (-7, 7) and (-7, -7), so this is not a function either.
• Option C) also has two pairs with the same first element (-9, 2) and (-9, -8), thus not representing a function.
• Option D) has all unique first elements, which makes this set of ordered pairs a function.

Therefore, the correct answer is Option D because it follows the rule that a function must assign only one output to each input.