Absolute Value

The distance of a number from zero — always non-negative.

f(x) = |x − 1| — the V-shape and its transformations

a (stretch) = 1

h (shift →) = 1

k (shift ↑) = 0

Definition

The absolute value of a number is its distance from zero on the number line — it is always non-negative.

|x| = \begin{cases} x & \text{if } x \geq 0 \\ -x & \text{if } x < 0 \end{cases}

Examples: $|5| = 5$ , $|-5| = 5$ , $|0| = 0$ .

Distance interpretation

$|{-8}|$ asks: how far is $-8$ from $0$ ? The answer is $8$ .

$|3 - 7|$ asks: how far apart are $3$ and $7$ ? $|{-4}| = 4$ .

Try it

Solve $|x| = 6$ .

Solution

$|x| = 6$ means $x = 6$ or $x = -6$ .

Related concepts