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

A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.

{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)} - it's a function

{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)} - it's a function

{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)} - it's a function

{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)} - it's not a function

Answer 2

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

Explanation:

Given the set, it will be a function if each point in x-axis has only one value in the y-axis, i.e exist a unique value to each point in the x-axis.

In our case, we can see in the pic the graph representation of each set with a color

{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)} -> Green points

{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)} -> Blue points

{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)} -> Black point s

{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)} -> Red points

According to the graph, the only set that had only one value from x-axis is the second set (Blue points).