How do you know whether a relation is a function?
By determining if each value from one set maps to another set such that each element of the domain pairs with exactly two elements of the range.
By determining if each value from one set maps to another set such that each element of the domain pairs with exactly two elements of the range.
By determining if each value from one set maps to another set such that exactly one element of the domain pairs with exactly one element of the range.
By determining if each value from one set maps to another set such that exactly one element of the domain pairs with exactly one element of the range.
By determining if each value from one set maps to another set such that each element of the domain pairs with exactly one element of the range.
By determining if each value from one set maps to another set such that each element of the domain pairs with exactly one element of the range.
By determining if each value from one set maps to another set such that one element of the domain pairs with exactly two elements of the range.
By determining if each value from one set maps to another set such that exactly one element of the domain pairs with exactly one element of the range.
The correct answer is: By determining if each value from one set maps to another set such that each element of the domain pairs with exactly one element of the range.
To determine whether a relation is a function, you need to consider how each value from one set (the domain) is mapped to another set (the range).
A relation is a function if each element of the domain pairs with exactly one element of the range. This means that for every input value in the domain, there should be exactly one output value in the range.
If there is an element in the domain that maps to more than one element in the range, then the relation is not a function. Similarly, if there is an element in the domain that does not have any corresponding element in the range, then the relation is also not a function.
Essentially, to check if a relation is a function, you need to ensure that each element in the domain has a unique mapping to an element in the range, and no element in the domain is left unmapped or has multiple mappings.
So, out of the provided options:
- By determining if each value from one set maps to another set such that each element of the domain pairs with exactly two elements of the range: This option is incorrect because a function should have each element of the domain pairing with exactly one element of the range, not two.
- By determining if each value from one set maps to another set such that exactly one element of the domain pairs with exactly one element of the range: This option is correct and aligns with the definition of a function.
- By determining if each value from one set maps to another set such that each element of the domain pairs with exactly one element of the range: This option is also correct and aligns with the definition of a function.
- By determining if each value from one set maps to another set such that one element of the domain pairs with exactly two elements of the range: This option is incorrect because a function should have each element of the domain pairing with exactly one element of the range, not two.
Therefore, the correct options to determine whether a relation is a function are:
- By determining if each value from one set maps to another set such that exactly one element of the domain pairs with exactly one element of the range.
- By determining if each value from one set maps to another set such that each element of the domain pairs with exactly one element of the range.