# 004 Sample Final A, Problem 5

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Describe how the graph of can be obtained from a basic graph. Then sketch the graph. Provide at least two ordered pairs, and the equation of any asymptote.

Foundations |
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1) What is the basic graph of ? |

2) How is the graph obtained from ? |

3) How is the graph obtained from ? |

Answer: |

1) The basic graph is . |

2) The graph of is obtained by shifting the graph of up 1 unit. |

3) The graph of is obtained by shifting the graph of to the right by 3 units. |

Solution:

Step 1: |
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We start with the basic graph of . |

To get the graph of from , we shift the graph of down 2 and to the left by 1. |

Step 2: |
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Two ordered pairs are (-1,-1), and (0,1). There is a horizontal asymptote at . |

Final Answer: |
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To get the graph of from , we shift the graph of down 2 and to the left by 1. |

Two ordered pairs are (-1,-1), and (0,1). There is a horizontal asymptote at |