If a relation is a function, how many y-values can each x-value have?
Domain: {- 2,3,4,6} Range: {- 1,2,3} Is It a Function? Yes Is it one-to-one, onto, both, or neither? Onto
Practice makes perfect
For a relation to be a function, each x-value can only be paired with one y-value, but one y-value can be paired with multiple x-values.
Let's look at the given values.
x
y
- 2
3
4
- 1
3
2
6
3
Since each input x has only one output, the relation in the table is a function.
Now let's look for the domain and range of the given coordinate pairs. The domain of a function is found by listing the relation's x-values. The range is found by listing the relation's y-values.
Domain:& {- 2,3,4,6}
Range:& {- 1,2,3}
In order to determine if a function is one-to-one, onto, both, or neither, let's review what each of these types of relationship means.
One-to-one: Each element of the domain is paired with exactly one unique element of the range.
Onto: Every element in the range must be paired with at least one element of the domain.
Both: Each element of the domain is paired with exactly one element of the range and each element in the range is paired with exactly one element in the domain.
Observing the given table, we see that elements in the range are paired with multiple elements in the domain. This means that the function is not one-to-one. On the other hand, each element of the range corresponds to at least one element in the domain. Therefore, the function is onto.
