Piecewise Functions Worksheets
Evaluate and transform functions while keeping the input order and domain explicit.
Before you begin
Evaluate functions, solve for variables and use exponential/logarithmic inverses.
Worked example
f(x) = 4x + 7 for x < 3, and f(x) = x² for x ≥ 3. Find f(-3).
- Since -3 < 3, use the first branch.
- Substitute into that branch only.
Answer: -5
Check your result using the method in the example before moving to the next question.
Choose your level
These sets use the same exercise types and number ranges across level labels. Choose a fresh set for additional practice.
- Easy: Start with the preview and follow the worked example.
- Medium: Practice the same exercise types with a fresh numbered set.
- Hard: Use another set to practice explaining and checking your answers.
Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.
Preview and print an easy set
Try six questions below, or choose a full set at your level.
1
f(x) = 3x + 4 for x < 5, and f(x) = x² for x ≥ 5. Find f(2).
2
f(x) = 2x + 4 for x < 7, and f(x) = x² for x ≥ 7. Find f(1).
3
f(x) = 2x + 6 for x < 3, and f(x) = x² for x ≥ 3. Find f(-1).
4
f(x) = 6x + 8 for x < 2, and f(x) = x² for x ≥ 2. Find f(5).
5
f(x) = 8x + 3 for x < 6, and f(x) = x² for x ≥ 6. Find f(0).
6
f(x) = 3x + 1 for x < 1, and f(x) = x² for x ≥ 1. Find f(-2).
Answer Key
1. 102. 63. 44. 255. 36. -5