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

Aug 31, 2016

The relation $\left\mid y - x \right\mid = 1$ 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:

$\left\mid y - x \right\mid = 1$

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 $y = - 1$