Rational Functions Unit Test - LibertyPrecal



Rational Functions Practice name ___________________

Multiple Choice

____ 1. Which of the following has a horizontal asymptote at [pic]?

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |all of the above |

____ 2. Which function has vertical asymptotes [pic] and [pic]?

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |all of the above |

____ 3. What is the equation for the horizontal asymptote of the graph of the function shown?

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |[pic] |

____ 4. What are the x-intercepts of the graph of [pic]?

|a. |–4, 5 |c. |4, –5 |

|b. |–7, 3 |d. |7, –3 |

____ 5. Which of the following functions has a hole at x = 5?

|a. |[pic] |c. |[pic] |

|b. |[pic] |d. |B and C |

Problem Solving

6. Explain how the graph of [pic] is the same and different from the graph of [pic].

7. Graph the following: [pic]

8. [pic]

9. Graph the following: [pic]

Without graphing these, find the equation that:

______10. Has a vertical asymptote at x = -3 and horizontal asymptote at y =0.

______11. Has both a vertical and horizontal asymptote but no removable

discontinuity.

______12. Has a removable discontinuity but no asymptotes.

______13. Has it all, both asymptotes and a removable discontinuity.

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Hole __________

HA/SA__________

VA___________

Domain________________

Range_________________

x int _________________

y int _________________

Hole __________

HA/SA__________

VA___________

Domain________________

Range_________________

x int _________________

y int _________________

Hole __________

HA/SA__________

VA___________

Domain________________

Range_________________

x int _________________

y int _________________

A) y = [pic]

B) y = [pic]

C) y = [pic]

D) y = [pic]

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