Linear and Nonlinear Functions Worksheets
Connect functions with inputs, outputs, equations, slopes and coordinate graphs.
Before you begin
Read ordered pairs and solve linear equations using signed arithmetic.
Worked example
Is y = 1x + 1 linear or nonlinear? Explain.
- A linear equation in this form has only a first power of x.
Answer: Linear; it has a constant rate of change.
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
Is y = 1x - 1 linear or nonlinear? Explain.
2
Is y = 2x² - 2 linear or nonlinear? Explain.
3
Is y = 2x + 0 linear or nonlinear? Explain.
4
Is y = 2x² - 1 linear or nonlinear? Explain.
5
Is y = 2x + 2 linear or nonlinear? Explain.
6
Is y = 2x² + 2 linear or nonlinear? Explain.
Answer Key
1. Linear; it has a constant rate of change.2. Nonlinear; a nonzero squared term gives a changing rate of change.3. Linear; it has a constant rate of change.4. Nonlinear; a nonzero squared term gives a changing rate of change.5. Linear; it has a constant rate of change.6. Nonlinear; a nonzero squared term gives a changing rate of change.