Question

Is every relation a function? Is every function a

relation?

Short answer

Every relation is not a function. Every function is a relation.

Step-by-step solution

Step 1. Given information.

A relation is a function when each input has exactly only one output. A relation is the set of inputs to the set of outputs. all functions are relations but all the relations are not functions.

So, every relation is not a function but every function is a relation.

Step 2. Example relation.

Now, write one example for "function" and one example for "not a function".

In the first diagram, we can say that each input has only one output. So this relation is a function.

In the second diagram, input 5 has two outputs 4 and 7 . So it is not a function but there are a set of inputs and outputs. Hence we say it is a relation. This relation is not a function.

Every relation is not a function but every function is a relation.