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Overview
Grade 12 Advanced Functions, University Preparation (MHF4U)
D. Characteristics of Functions
61. 12AF.D3.2
61.2 Evaluating piecewise functions
Evaluating Piecewise Functions
Learn how to evaluate piecewise functions by identifying which rule applies to a given x-value and substituting correctly, with worked examples.
What You'll Learn
Identify which interval an x-value belongs to before choosing a rule to substitute into.
Apply only the piece of the function whose domain restriction includes the given input.
Substitute the x-value into the matching expression and simplify to find the output.
Recognize boundary values written with strict versus non-strict inequalities such as less than versus less than or equal to.
Check your answer by confirming the chosen interval truly contains the number you plugged in.
What You'll Practice
1
Evaluating piecewise functions with two or three sub-functions
2
Working with domains defined by inequalities and interval notation
3
Handling boundary values and equal signs in domain conditions
4
Calculating outputs using various function types including polynomials and radicals
Why This Matters
Piecewise functions appear throughout calculus, economics, and real-world applications like tax brackets and shipping rates. Mastering how to evaluate them builds your ability to work with functions that change behavior based on different conditions.
Before You Start — Make Sure You Can:
This Unit Includes
16 Video lessons
Learning resources
Skills
Piecewise Functions
Domain
Function Evaluation
Interval Notation
Inequalities
Sub-functions
ON Curriculum Aligned