# Difference between revisions of "005 Sample Final A, Question 18"

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! Foundations | ! Foundations | ||

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− | |1) What is the basic graph of <math> f(x) = 3^{ | + | |1) What is the basic graph of <math> f(x) = \left(\frac{1}{3}\right)^{x+1} + 1</math>? |

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− | |2) How is the graph <math>g(x)=x+1</math> obtained from <math>f(x)=x</math>? | + | |2) How is the graph <math>g(x)=x^3+1</math> obtained from <math>f(x)=x^3</math>? |

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− | |3) How is the graph <math>g(x)=(x | + | |3) How is the graph <math>g(x)=(x+1)^2</math> obtained from <math>f(x)=x^2</math>? |

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|Answer: | |Answer: | ||

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− | |1) The basic graph is <math>y=3^x</math>. | + | |1) The basic graph is <math>y=\left(\frac{1}{3}\right)^x</math>. |

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|2) The graph of <math>g(x)</math> is obtained by shifting the graph of <math>f(x)</math> up 1 unit. | |2) The graph of <math>g(x)</math> is obtained by shifting the graph of <math>f(x)</math> up 1 unit. | ||

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− | |3) The graph of <math>g(x)</math> is obtained by shifting the graph of <math>f(x)</math> to the | + | |3) The graph of <math>g(x)</math> is obtained by shifting the graph of <math>f(x)</math> to the left by 1 unit. |

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! Step 1: | ! Step 1: | ||

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− | |We start with the basic graph of <math>g(x)=3^x</math>. | + | |We start with the basic graph of <math>g(x)=\left(\frac{1}{3}\right)^x</math>. |

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− | |To get the graph of <math>f(x)</math> from <math>g(x)</math>, we shift the graph of <math>g(x)</math> | + | |To get the graph of <math>f(x)</math> from <math>g(x)</math>, we shift the graph of <math>g(x)</math> up 2 and to the left by 1. |

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! Step 2: | ! Step 2: | ||

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− | |Two ordered pairs are ( | + | |Two ordered pairs are <math>\left(0, \frac{4}{3}\right)</math> and <math>(-1, 1)</math>. There is a horizontal asymptote at <math>y = 1</math>. |

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! Final Answer: | ! Final Answer: | ||

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− | |To get the graph of <math>f(x)</math> from <math>3^x</math>, we shift the graph of <math>3^x</math> | + | |To get the graph of <math>f(x)</math> from <math>\left(\frac{1}{3}\right)^x</math>, we shift the graph of <math>\left(\frac{1}{3}\right)^x</math> up 1 and to the left by 1. |

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− | [[File: | + | [[File:5_Sample_Final_18.png]] |

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[[005 Sample Final A|'''<u>Return to Sample Exam</u>''']] | [[005 Sample Final A|'''<u>Return to Sample Exam</u>''']] |

## Latest revision as of 11:56, 2 June 2015

** Question ** Graph the following function,

Make sure to label any asymptotes, and at least two points on the graph.

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 left by 1 unit. |

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 up 2 and to the left by 1. |

Step 2: |
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Two ordered pairs are and . There is a horizontal asymptote at . |

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