End Behavior and Asymptotes 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
For f(x) = (4x + 7)/(x − 3), find vertical and horizontal asymptotes.
- At x = 3, the denominator is zero and the numerator 19 is nonzero.
- Equal numerator/denominator degrees give the ratio of leading coefficients as the horizontal asymptote.
Answer: Vertical: x = 3. Horizontal: y = 4.
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
For f(x) = (3x + 4)/(x − 5), find vertical and horizontal asymptotes.
2
For f(x) = (2x + 4)/(x − 7), find vertical and horizontal asymptotes.
3
For f(x) = (2x + 6)/(x − 3), find vertical and horizontal asymptotes.
4
For f(x) = (6x + 8)/(x − 2), find vertical and horizontal asymptotes.
5
For f(x) = (8x + 3)/(x − 6), find vertical and horizontal asymptotes.
6
For f(x) = (3x + 1)/(x − 1), find vertical and horizontal asymptotes.
Answer Key
1. Vertical: x = 5. Horizontal: y = 3.2. Vertical: x = 7. Horizontal: y = 2.3. Vertical: x = 3. Horizontal: y = 2.4. Vertical: x = 2. Horizontal: y = 6.5. Vertical: x = 6. Horizontal: y = 8.6. Vertical: x = 1. Horizontal: y = 3.