The Absolute Value Function
The absolute value function: 𝑓(𝑥) = |𝑥|
→ On a number line, this function describes the distance or magnitude of the
the number x from the origin
→ 𝑓(𝑥) = |𝑥| is a piecewise function in which 𝑓(𝑥) = �
−𝑥, 𝑥 < 0
𝑥, 𝑥 ≥ 0
Example 1: |3| =
|−2| =
|−3| =
Example 2: Find
|−2−4|+2
|4|
=
Example 3: Express using absolute value notation.
a)
𝑥 ≤ −2 𝑜𝑟 𝑥 ≥ 2
b)
−5 ≤ 𝑥 ≤ 5
b)
|𝑥| ≤ 5
Example 4: Graph on a number line.
a)
|𝑥| > 4
Example 5: Rewrite using absolute value notation.
a)
b)
Example 6: Graph 𝑓(𝑥) = |𝑥 − 2|
Example 7: Graph 𝑓(𝑥) = |𝑥| + 2
Example 8: Graph 𝑓(𝑥) = |3𝑥 − 6|