# How do you decide whether the relation abs(x)-y=5 defines a function?

Jul 9, 2017

As $x$ is the independent variable and any 1 value of $x$ gives only 1 answer for $y$ this is a function

This is called a one-to-one mapping

#### Explanation:

Make $x$ the independent variable and $y$ the dependent (the answer)

Add $y$ to both sides

$| x | = 5 + y$

Subtract 5 from both sides

$y = | x | - 5$

As $x$ is the independent variable and any 1 value of $x$ gives only 1 answer for $y$ this is a function

This is called a one-to-one mapping