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Overview
Grade 12 Advanced Functions, University Preparation (MHF4U)
D. Characteristics of Functions
61. 12AF.D3.2
61.3 Graphing piecewise linear functions
Graphing Piecewise Linear Functions
Master the process of graphing piecewise linear functions: matching each linear piece to its domain, marking open or closed circles, and joining the pieces correctly.
What You'll Learn
Identify each rule in a piecewise linear function along with its restricted domain
Graph each linear piece only over the x-values allowed by its own domain condition
Decide between an open circle and a closed circle at each boundary point based on the inequality symbol
Recognize a jump discontinuity when the pieces do not meet at the same y-value
Apply the vertical line test to confirm the combined graph is still a valid function
Connect graphing piecewise linear functions to the special case of absolute value graphs
What You'll Practice
1
Graphing piecewise functions with two or three sub-functions and correct endpoint notation
2
Finding domain and range from piecewise function graphs
3
Writing piecewise function equations from given V-shaped and segmented graphs
4
Converting absolute value functions to piecewise notation with proper domains
Why This Matters
Graphing piecewise functions is essential for modeling real-world situations that change behavior at specific points, like tax brackets, shipping rates, or parking fees. You'll use these skills in calculus, economics, and engineering to analyze functions with different rules over different intervals.
Before You Start — Make Sure You Can:
This Unit Includes
12 Video lessons
Learning resources
Skills
Piecewise Functions
Graphing
Domain and Range
Absolute Value
Linear Functions
Function Notation
Interval Notation
ON Curriculum Aligned