Overview
Watch
Read
Next Steps
Overview
Mathematics Essentials 11
Patterns and Relations
7. Model real-world problems using functions, equations, inequalities and discrete structures
7.11 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
NS Curriculum Aligned