If a relation is a function, how many y-values can an x-value have?
Yes, see solution.
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. In a mapping, the x-values in the domain can only point to one y-value in the range.
In the given mapping, we can see that none of the x-values correspond to multiple y-values. Since all of the values in the domain only point to one value in the range, the relation is a function.
Extra
Injective, Surjective, and Bijective Functions
In higher level math courses, functions are often categorized in three different ways.
One-to-one: Each element of the domain is paired with exactly one unique element of the range. In other words, this type of function would pass a horizontal line test. The formal name for this type of function is injective.
Onto: Every element in the range must be paired with at least one element of the domain. The formal name for this type of function is surjective.
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. The formal name for this type of function is bijective.
Our function is onto because each element in the range pairs with at least one element in the domain. It is not one-to-one because multiple values in the domain point to the same values in the range.
