Question

Which set of ordered pairs represents a function?

{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)}
{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}
{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)}
{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)}

Answer 1

{(3, -1), (7,1), (-6,-1), (9,1), (2,-1)} is the right answer because each input has only one output.  (none of the x's repeat).

Answer 2

{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}

Explanation:

A set of ordered pairs in the format
`(x,y)` represents a function if for each value of x, there is only one value for y.

The first set of ordered pairs is:

{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)}

There are two values of y for
`x = 1`. This means that this set of ordered pairs does not represent a function.

The second set of ordered pairs is:

{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}

For each value of x here, there is only one value of y. This means that this set of ordered pairs represents a function. This is the answer.

The third set of ordered pairs is:

{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)}

There are two values of y for
`x = -2`. This means that this set of ordered pairs does not represent a function.

The fourth set of ordered pairs is:

{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)}

There are two values of y for
`x = -3`. This means that this set of ordered pairs does not represent a function.