Question

Which of the following represents a function?

Answer 1

Only the last example.

Explanation:

All of the examples define relations between a domain and range.

Such a relation will be a function if and only if each value in the domain corresponds to at most one value in the range.

In the first example, the value `-1` in the domain is associated with two values in the range, namely `-5` and `1`.

In the second example, the value `-1` in the domain is associated with two values in the range, namely `7` and `1`.

In the third example, the value `3` in the domain is associated with two values in the range, namely `2` and `4`.

In the fourth example, each of the values in the domain is associated with one value in the range, so this describes a function. Note however that the values `-4` and `-7` are both mapped to `5`. So the function described is not one to one and consequently its inverse is not a function.