Question

How is a function different than a relation?

Answer 1

Explanation

• Difference between relation and function.

Relation and Function both are same except for one thing.

Relation can have repetitive domain while Function cannot. We can say that Function is a relation without repetitive domain.

Example of Relation

{(1,1),(1,3),(2,5),(2,6),(3,46),(3,90)}

This is a relation because there are same and repetitive domain.

Example of Function

{(1,1),(2,4),(3,9),(4,16),(5,25),(6,36),(7,49)}

This can be classified as relation as well but relation that is function. We can say that function is a subset of relation. Remember that functions are relations that don't have repetitive domain while relations that are not function (or just relations) can have repetitive or same domain.

Graph of Relation and Function

Relations can have graphs along with Functions. The problem is you might not see set of ordered pairs but graph instead.

How can we tell if the graph is a function or just only relation? The answer is to do line test.

1. First we draw a vertical line.
2. See if the line intercepts the graph just one point or more than one.

If the graph intercepts only one point then it is a function. Otherwise, no.