Question

Which relation is a function?

I. {(2, 4), (–1, 7), (3, 0), (5, 4)}
II. {(–3, 6), (–3, 6), (8, 6), (8, 10)}
III. {(4, 1), (–2, 5), (–8, 3), (4, 6)}

A. II and III
B. I only
C. II only
D. I and II

Answer 1

Functions are supposed to have all different x-values, right?

Answer 2

NOT true!
As long as the identical x-values correspond to the same y-value, it would be still a function.
Your reasoning works in this particular problem, but would not work for:
{(–3, 6), (–3, 6), (8, 6), (9, 10)}
Since there are two x-values equal to -3, would this be a function?

Answer 3

My course states the following:
"To determine whether a set of ordered pairs is a function, first look at just the x-values. If you see any repeating x-values, then the relation is not a function."

Answer 4

`"To determine whether a set of ordered pairs is a function, first look at just the x-values. If you see any repeating x-values, then the relation is not a function."`

This is a misconception that actually went in books! Sigh!

When there is a repeated x-value, you need to look at the y-value as well to see if they are also identical. If they are, they can be considered identical ordered pairs, and hence it is still a function.

What is important is that :
if you are given an x-value, there is EXACTLY one corresponding y-value.