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Graphing Rational Functions - Worksheet 8 - 11th Grade

Hard

Simplify rational expressions, solve rational equations and retain excluded domain values.

hard: Use another set to practice explaining and checking your answers.

18 problems · 25-30 minutes · Skills: rational functions, graphing, asymptotes

About This Worksheet

This hard-level worksheet contains 18 problems designed for 11th Grade students practicing graphing rational functions. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

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

  • Simplify rational expressions, solve rational equations and retain excluded domain values.
  • Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: For y = 1/(x + 2) + 2, find the vertical and horizontal asymptotes and two points for a sketch.
Solution Steps:
  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).
Tip: Check your result using the method in the example before moving to the next question.
1
For y = 1/(x - 2) + 1, find the vertical and horizontal asymptotes and two points for a sketch.
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Diagram not to scale.
2
For y = 1/(x + 0) - 2, find the vertical and horizontal asymptotes and two points for a sketch.
xy0−55
Diagram not to scale.
3
For y = 1/(x + 0) + 2, find the vertical and horizontal asymptotes and two points for a sketch.
xy0−55
Diagram not to scale.
4
For y = 1/(x - 1) + 1, find the vertical and horizontal asymptotes and two points for a sketch.
xy0−55
Diagram not to scale.
5
For y = 1/(x - 2) + 2, find the vertical and horizontal asymptotes and two points for a sketch.
xy0−55
Diagram not to scale.
6
For y = 1/(x - 2) - 2, find the vertical and horizontal asymptotes and two points for a sketch.
xy0−55
Diagram not to scale.
7
For y = 1/(x + 1) - 2, find the vertical and horizontal asymptotes and two points for a sketch.
xy0−55
Diagram not to scale.
8
For y = 1/(x + 2) + 1, find the vertical and horizontal asymptotes and two points for a sketch.
xy0−55
Diagram not to scale.
9
For y = 1/(x + 1) + 2, find the vertical and horizontal asymptotes and two points for a sketch.
xy0−55
Diagram not to scale.
10
For y = 1/(x - 1) - 1, find the vertical and horizontal asymptotes and two points for a sketch.
xy0−55
Diagram not to scale.
11
For y = 1/(x + 0) + 1, find the vertical and horizontal asymptotes and two points for a sketch.
xy0−55
Diagram not to scale.
12
For y = 1/(x - 1) - 2, find the vertical and horizontal asymptotes and two points for a sketch.
xy0−55
Diagram not to scale.
13
For y = 1/(x + 0) + 0, find the vertical and horizontal asymptotes and two points for a sketch.
xy0−55
Diagram not to scale.
14
For y = 1/(x - 1) + 0, find the vertical and horizontal asymptotes and two points for a sketch.
xy0−55
Diagram not to scale.
15
For y = 1/(x - 2) + 0, find the vertical and horizontal asymptotes and two points for a sketch.
xy0−55
Diagram not to scale.
16
For y = 1/(x + 2) - 2, find the vertical and horizontal asymptotes and two points for a sketch.
xy0−55
Diagram not to scale.
17
For y = 1/(x - 2) - 1, find the vertical and horizontal asymptotes and two points for a sketch.
xy0−55
Diagram not to scale.
18
For y = 1/(x + 1) - 1, find the vertical and horizontal asymptotes and two points for a sketch.
xy0−55
Diagram not to scale.

Answer Key

1. Vertical: x = 2. Horizontal: y = 1. Points (3, 2), (1, 0).2. Vertical: x = 0. Horizontal: y = -2. Points (1, -1), (-1, -3).3. Vertical: x = 0. Horizontal: y = 2. Points (1, 3), (-1, 1).4. Vertical: x = 1. Horizontal: y = 1. Points (2, 2), (0, 0).5. Vertical: x = 2. Horizontal: y = 2. Points (3, 3), (1, 1).6. Vertical: x = 2. Horizontal: y = -2. Points (3, -1), (1, -3).7. Vertical: x = -1. Horizontal: y = -2. Points (0, -1), (-2, -3).8. Vertical: x = -2. Horizontal: y = 1. Points (-1, 2), (-3, 0).9. Vertical: x = -1. Horizontal: y = 2. Points (0, 3), (-2, 1).10. Vertical: x = 1. Horizontal: y = -1. Points (2, 0), (0, -2).11. Vertical: x = 0. Horizontal: y = 1. Points (1, 2), (-1, 0).12. Vertical: x = 1. Horizontal: y = -2. Points (2, -1), (0, -3).13. Vertical: x = 0. Horizontal: y = 0. Points (1, 1), (-1, -1).14. Vertical: x = 1. Horizontal: y = 0. Points (2, 1), (0, -1).15. Vertical: x = 2. Horizontal: y = 0. Points (3, 1), (1, -1).16. Vertical: x = -2. Horizontal: y = -2. Points (-1, -1), (-3, -3).17. Vertical: x = 2. Horizontal: y = -1. Points (3, 0), (1, -2).18. Vertical: x = -1. Horizontal: y = -1. Points (0, 0), (-2, -2).

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This worksheet focuses on rational functions, graphing, asymptotes. It is designed for 11th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

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This worksheet contains 18 problems. It typically takes 25-30 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.