Question

What is the absolute value function?

Answer 1

`|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 `|"-"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.