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Pre-Calculus Elective 11 (MAT521E)
Logical Reasoning
9. Demonstrate understanding of logical reasoning
9.1 Absolute value functions
Absolute Value Function and Graph
See how the absolute value function turns into a V-shaped graph, how to write it piecewise, and how to shift, stretch, and flip it.
What You'll Learn
An absolute value function always outputs a distance from zero, so its value can never be negative.
The parent function f(x) = |x| graphs as a V shape with its vertex at the origin.
Every absolute value function can be rewritten as a piecewise function with two linear pieces.
The form f(x) = a|x - h| + k moves the vertex to (h, k) and controls how wide or narrow, and which way up, the V opens.
Reading a table of values is one of the most reliable ways to plot an absolute value graph by hand.
What You'll Practice
1
Evaluating absolute values of integers, negatives, and nested expressions
2
Converting absolute value of linear expressions into two-piece piecewise functions
3
Converting absolute value of quadratic expressions into three-piece piecewise functions
4
Using test values to determine signs across different domain regions
Why This Matters
Absolute value functions are essential for modeling real-world situations involving distance, magnitude, and error. You'll use them in physics, engineering, and economics, and they're foundational for calculus concepts like limits and continuity.
Before You Start — Make Sure You Can:
This Unit Includes
4 Video lessons
Practice exercises
Learning resources
Skills
Absolute Value
Piecewise Functions
Number Line
Domain Analysis
Quadratic Expressions
Sign Rules
Function Notation
PEI Curriculum Aligned