Question

What is the difference between a relation

and a function? Is every relation a function? Is every
function a relation? Explain.
​

Answer 1

Not all relationships are functions, but all functions are also relationships

Explanation:

A relationship is a correspondence between two sets of values.

A relationship assigns values from an output set called range to a set and input called a domain.

On the other hand, a relation is a function if and only if there is only one value of the output set (Range) assigning to each value of the input set (Domain).

In other words, if an input value
`x_1` is assigned two or more output values
`y_1`,
`y_2`,
`y_3` .. then the relationship is not a function. This means that not all relationships are functions.

`y=\±√(x) +3` is a relation but it is not a function.

because when x = 4 then y = 1 and y = 5.

Not all relationships are functions, but all functions are also relationships