Question

Tell whether the relation is a function.

Explain.
{(−4, 0), (−3, 0), (−2, 1), (1, −2), (−3, 4)}

Answer 1

Explanation:

The easiest way to tell if a relation is a function is to look at the x coordinates. If none of them are the same in the set, then the relation is a function. If any of the x values are used more than once in the set, it is only a relation. This set uses -3 two times, so it is a relation.

Answer 2

It is not a function.

Explanation:

A function is a relation in which each input x has only one output y.

One visual way to tell the difference is to plot the relation and use the vertical line test.

If a vertical line for a given value of x passes through more than one point, the relation is not a function.

We see in the diagram that the line x = -3 includes (-3,0) and (-3,4), so the relation is not a function.