Composition of Functions - Worksheet 7 - 12th Grade
MediumFind and evaluate composite functions (Medium)
22 problems · 20-25 minutes · Skills: functions, composition, domain
About This Worksheet
This medium-level worksheet contains 22 problems designed for 12th Grade students practicing composition of functions. Medium worksheets introduce larger numbers and varied question formats to deepen understanding and build fluency.
Function composition is the mathematical description of applying one process after another — a concept fundamental to computer science (function pipelines), engineering (system analysis), and calculus (the Chain Rule describes the derivative of a composite function).
- Evaluate a composite function for specific values and general expressions
- Determine the domain of a composite function, considering restrictions from both component functions
- Decompose a given function into two simpler functions as a sum or composition
- Evaluate (f ∘ g)(x) and (g ∘ f)(x) and explain why they differ
- Recognize function composition structure in real-world two-step processes
How to Solve: Worked Example
- Read the problem carefully.
- Identify what is being asked.
- Use what you know to find the answer.
- Check your work.
Answer Key
Frequently Asked Questions
How do I download this composition of functions - worksheet 7 worksheet?
Click the "Download PDF / Print" button at the top of the worksheet. You can save it as a PDF or print it directly. The answer key will be on a separate page.
How do I find worksheets at different difficulty levels?
Each subtopic has 10 worksheets: Worksheets 1-3 are Easy, 4-7 are Medium, and 8-10 are Hard. Start with Easy worksheets to build confidence, then progress to harder ones.
What skills does this functions & their graphs worksheet cover?
This worksheet focuses on functions, composition, domain. It is designed for 12th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.
Can I use this worksheet in my classroom?
Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.
How many problems are on this worksheet?
This worksheet contains 22 problems. It typically takes 20-25 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.