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

1 Answer
Aug 31, 2016

Answer:

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#