Question

Which of the following relations describes a function?

A. {(-3,0), (0, 3), (3, 0), (0, -3)}
B. {(16,-4), (9, -3), (9, 3), (16,4)}
C. {(3,-3), (0, 0), (3, 3), (4,4)}
D. {(-4, 16), (-3, 9), (3, 9), (4, 16)}

Please choose the option that represents a function.

Answer 1

Option D {(-4, 16), (-3, 9), (3, 9), (4, 16)} is the correct choice as it represents a function. This is because each x-value is paired with only one y-value.

Step-by-step explanation:

To determine which set of ordered pairs describes a function, we must look at each pair to make sure that every input (or x-value) has exactly one output (or y-value). In other words, each x-value must be paired with only one y-value.

• A. {(-3,0), (0, 3), (3, 0), (0, -3)} has the x-value of 0 paired with two different y-values (3 and -3), so it is not a function.
• B. {(16,-4), (9, -3), (9, 3), (16,4)} also has repeated x-values (9 and 16) with different corresponding y-values, so it is not a function.
• C. {(3,-3), (0, 0), (3, 3), (4,4)} also has the x-value 3 paired with two different y-values (-3 and 3), so it is not a function.
• D. {(-4, 16), (-3, 9), (3, 9), (4, 16)} has unique y-values for each x-value. Thus, option D is the correct choice as it represents a function.