Which of the following represents a function

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.

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