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

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

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Answer 1 · 2016-08-31T22:44:38

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

Explanation:

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

The equation:

$| y - x | = 1$ $abs(y-x) = 1$

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

Here is its graph:

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

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

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

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