Graphing Rational Functions Worksheets

Before you begin

Factor polynomials, use exponent laws and solve equations with domain restrictions.

Worked example

For y = 1/(x + 2) + 2, find the vertical and horizontal asymptotes and two points for a sketch.

1. The denominator is zero at the vertical asymptote.
2. As |x| grows, the reciprocal term approaches zero.
3. Evaluate one unit to each side of the vertical asymptote.

Answer: Vertical: x = -2. Horizontal: y = 2. Points (-1, 3), (-3, 1).

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.

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Try six questions below, or choose a full set at your level.

Full worksheet sets

Practice next

• Factoring Higher-Degree Polynomials
• Polynomial Operations
• Polynomial Remainder and Factor Theorems