# What is the absolute value function?

Mar 24, 2017

$| x - h | = k$ means what numbers $x$ are $k$ away from $h$

#### Explanation:

Just as a function, $| x |$ is the value of $x$ without the sign, in other words the distance between $0$ and $x$.

For example, $| 5 | = 5$ and $| \text{-} 5 | = 5$.

In an equation, $| x - h | = k$ means what numbers $x$ are $k$ away from $h$.

For example, solving $| x - 3 | = 5$ for $x$ asks what numbers are 5 away from 3: intuitively the answers are 8 (3+5) and -2 (3-5). Plugging these numbers in for $x$ confirms their accuracy.