Question

Which set of points would NOT define a function?

A. {(-2,-2), (-1,-1), (0, 0), (1, 1), (2, 2)}
B. {(-2, 9), (0, 1), (1.0), (3, 4), (4, 9)}
C. {(-1,0), (0, 1), (0, -1), (3, 2), (3,-2)}
D. {(-6, 2), (-5, 1), (-4, 0), (-3, 1), (-2, 2)}

Answer 1

A set of points does not define a function if there are two or more points with the same x-value but different y-values. Option C, {(-1,0), (0, 1), (0, -1), (3, 2), (3,-2)}, does NOT define a function.

Step-by-step explanation:

In order for a set of points to define a function, each input (x-value) must have exactly one output (y-value). Therefore, a set of points does not define a function if there are two or more points with the same x-value but different y-values.

Looking at the options:

• A. {(-2,-2), (-1,-1), (0, 0), (1, 1), (2, 2)}: This set defines a function because each x-value has exactly one y-value.
• B. {(-2, 9), (0, 1), (1,0), (3, 4), (4, 9)}: This set defines a function because each x-value has exactly one y-value.
• C. {(-1,0), (0, 1), (0, -1), (3, 2), (3,-2)}: This set does NOT define a function because the x-value of 0 has two different y-values (0 and -1).
• D. {(-6, 2), (-5, 1), (-4, 0), (-3, 1), (-2, 2)}: This set defines a function because each x-value has exactly one y-value.

Therefore, option C, {(-1,0), (0, 1), (0, -1), (3, 2), (3,-2)}, does NOT define a function.