End Behavior & Asymptotes Worksheet 6

Evaluate and transform functions while keeping the input order and domain explicit.

medium: Practice the same exercise types with a fresh numbered set.

18 problems · 20-25 minutes · Skills: functions, asymptotes, end behavior

About This Worksheet

This medium-level worksheet contains 18 problems designed for 12th Grade students practicing end behavior & asymptotes. Medium worksheets introduce larger numbers and varied question formats to deepen understanding and build fluency.

Evaluate functions, solve for variables and use exponential/logarithmic inverses.

Evaluate and transform functions while keeping the input order and domain explicit.
Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: For f(x) = (4x + 7)/(x − 3), find vertical and horizontal asymptotes.

Solution Steps:

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.

Tip: Check your result using the method in the example before moving to the next question.

Paper Include separate answer key in PDF

For f(x) = (3x + 8)/(x − 8), find vertical and horizontal asymptotes.

For f(x) = (4x + 1)/(x − 8), find vertical and horizontal asymptotes.

For f(x) = (5x + 9)/(x − 5), find vertical and horizontal asymptotes.

For f(x) = (5x + 6)/(x − 4), find vertical and horizontal asymptotes.

For f(x) = (6x + 4)/(x − 2), find vertical and horizontal asymptotes.

For f(x) = (6x + 9)/(x − 4), find vertical and horizontal asymptotes.

For f(x) = (7x + 9)/(x − 5), find vertical and horizontal asymptotes.

For f(x) = (4x + 8)/(x − 7), find vertical and horizontal asymptotes.

For f(x) = (3x + 1)/(x − 4), find vertical and horizontal asymptotes.

For f(x) = (7x + 1)/(x − 3), find vertical and horizontal asymptotes.

For f(x) = (6x + 4)/(x − 8), find vertical and horizontal asymptotes.

For f(x) = (6x + 2)/(x − 4), find vertical and horizontal asymptotes.

For f(x) = (2x + 6)/(x − 3), find vertical and horizontal asymptotes.

For f(x) = (3x + 2)/(x − 7), find vertical and horizontal asymptotes.

For f(x) = (3x + 8)/(x − 7), find vertical and horizontal asymptotes.

For f(x) = (2x + 2)/(x − 2), find vertical and horizontal asymptotes.

For f(x) = (4x + 3)/(x − 6), find vertical and horizontal asymptotes.

For f(x) = (8x + 2)/(x − 7), find vertical and horizontal asymptotes.

Answer Key

1. Vertical: x = 8. Horizontal: y = 3.2. Vertical: x = 8. Horizontal: y = 4.3. Vertical: x = 5. Horizontal: y = 5.4. Vertical: x = 4. Horizontal: y = 5.5. Vertical: x = 2. Horizontal: y = 6.6. Vertical: x = 4. Horizontal: y = 6.7. Vertical: x = 5. Horizontal: y = 7.8. Vertical: x = 7. Horizontal: y = 4.9. Vertical: x = 4. Horizontal: y = 3.10. Vertical: x = 3. Horizontal: y = 7.11. Vertical: x = 8. Horizontal: y = 6.12. Vertical: x = 4. Horizontal: y = 6.13. Vertical: x = 3. Horizontal: y = 2.14. Vertical: x = 7. Horizontal: y = 3.15. Vertical: x = 7. Horizontal: y = 3.16. Vertical: x = 2. Horizontal: y = 2.17. Vertical: x = 6. Horizontal: y = 4.18. Vertical: x = 7. Horizontal: y = 8.

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Frequently Asked Questions

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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, asymptotes, end behavior. 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 18 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.