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Overview
Grade 12 Advanced Functions, University Preparation (MHF4U)
D. Characteristics of Functions
61. 12AF.D3.2
61.4 Graphing piecewise non-linear functions
Graphing Piecewise Non-Linear Functions
Master a clear method for graphing piecewise functions built from parabolas, square roots, and exponential curves instead of straight lines.
What You'll Learn
Split the domain of a piecewise non-linear function into the intervals given by each rule.
Identify each piece as a known curve type, such as a parabola, square root, or exponential function.
Check the boundary x-value in each piece to decide whether it gets an open circle or a closed circle.
Sketch each curve using only the portion of it that falls inside its own restricted domain.
Compare the two pieces at the boundary to decide whether the graph is continuous or has a jump.
Combine the separate sketches into one graph that represents the whole piecewise function.
What You'll Practice
1
Sketching piecewise functions with parabolas, cubics, reciprocals, and radical functions
2
Finding domain and range from graphs using interval and set notation
3
Converting absolute value functions into equivalent piecewise definitions
4
Graphing transformations of nonlinear functions with restricted domains
Why This Matters
Piecewise nonlinear functions model real-world situations where relationships change at different thresholdslike tax brackets, shipping rates, or water pressure at varying depths. Mastering these graphs builds your ability to analyze complex functions in calculus and applied math.
Before You Start — Make Sure You Can:
This Unit Includes
13 Video lessons
Learning resources
Skills
Piecewise Functions
Nonlinear Graphs
Domain and Range
Absolute Value
Parabolas
Cubic Functions
Transformations
Graphing
ON Curriculum Aligned