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Definition
An absolute value function is any function that contains an expression inside absolute value bars, typically written as:
The absolute value of a number represents its distance from zero on the number line, so it is always non-negative.
Formally:

Summary
General Form

Graph Shape

Transformations

Absolute Value Inequalities

Why They Matter
Absolute value functions appear in real-life situations involving:
- distance
- error or tolerance
- piecewise behavior
- optimization problems
They are also a foundation for more advanced math, including piecewise-defined functions and linear programming.
Absolute Value Functions Math Activities
This is a fantastic bundle which includes 10 activities with answer guides about Absolute Value Functions. All our worksheets are completely editable so can be tailored for your curriculum and target audience.
Resource Examples
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Worksheets Activities Included
- Identify the Vertex and Slope from an Equation
- Graph Absolute Value Functions
- Convert Between Piecewise and Absolute Value Form
- Solve Basic Absolute Value Equations
- Solve Absolute Value Inequalities
- Write an Absolute Value Function from a Graph
- Determine Transformations
- Evaluate Absolute Value Functions
- Modeling Real-World Situations
- Compare Two Absolute Value Functions