# Absolute value functions

### Absolute value functions

Absolute value is basically the distance between "number" and "zero" on a number line. We will look into this concept in this lesson. We will also learn how to express absolute value functions as piecewise functions.

#### Lessons

Definition of “Absolute Value”: | number | = distance between “ number ” and “zero”
• 1.
Review: Evaluating the Absolute Value of a Number
Evaluate:
i) $\left| { - 5} \right|$
ii) $\left| 5 \right|$
iii) $\left| 0 \right|$
iv) $- \left| 6 \right|$
v) $- \left| { - 6} \right|$
vi) $\left| 3 \right| + {\;}\left| { - 3} \right|$
vii) $\left| {2 - 9} \right|$
viii) $- \left| { - \sqrt {16} } \right|$

• 2.
Evaluating Expressions Involving Absolute Values

Evaluate:

i) $|13-23|-12$

ii) $|\; |4|-|8|\;|$

iii) $| {^3}\sqrt{-27}|$

• 3.
Expressing an Absolute Value Linear Function as a Piecewise Function

Express the absolute value function as a piecewise function: $g\left( x \right) = \left| {5 - 4x} \right|$

• 4.
Expressing an Absolute Value Quadratic Function as a Piecewise Fu nction

Express the absolute value function as a piecewise function: $f\left( x \right) = \left| {x^2 - 4} \right|$