Does the equation abs(y-x) = 1 define a function?

1 Answer
Aug 31, 2016

The relation abs(y-x)=1 does not describe a function since it does not result in a unique value of y for each value of x in its domain.

Explanation:

A relation is a function if it defines at most one value of y for each value of x.

The equation:

abs(y-x) = 1

describes a relation between x and y which does not result in a unique value of y for all values of x. In fact for any x there are two possible values of y.

Here is its graph:

graph{abs(y-x)=1 [-5, 5, -2.5, 2.5]}

So for example, if x=0 then y = 1 or y = -1