Function Transformations 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
Describe the transformations from y = x² to y = 4(x − 7)² + 3.
- A subtraction inside the input shifts the graph right.
- The outside multiplier stretches vertically.
- The outside constant shifts vertically.
Answer: Shift right 7, stretch vertically by 4, and shift up 3.
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
Describe the transformations from y = x² to y = 3(x − 4)² + 5.
2
Describe the transformations from y = x² to y = 2(x − 4)² + 7.
3
Describe the transformations from y = x² to y = 2(x − 6)² + 3.
4
Describe the transformations from y = x² to y = 6(x − 8)² + 2.
5
Describe the transformations from y = x² to y = 8(x − 3)² + 6.
6
Describe the transformations from y = x² to y = 3(x − 1)² + 1.
Answer Key
1. Shift right 4, stretch vertically by 3, and shift up 5.2. Shift right 4, stretch vertically by 2, and shift up 7.3. Shift right 6, stretch vertically by 2, and shift up 3.4. Shift right 8, stretch vertically by 6, and shift up 2.5. Shift right 3, stretch vertically by 8, and shift up 6.6. Shift right 1, stretch vertically by 3, and shift up 1.