# Difference between revisions of "005 Sample Final A, Question 19"

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|1) The amplitude is A, the period is <math>\frac{2\pi}{B}</math>, the horizontal shift is left by C units if C is positive and right by C units if C is negative, the vertical shift is up by D if D is positive and down by D units if D is negative. | |1) The amplitude is A, the period is <math>\frac{2\pi}{B}</math>, the horizontal shift is left by C units if C is positive and right by C units if C is negative, the vertical shift is up by D if D is positive and down by D units if D is negative. | ||

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− | |2) | + | |2) The five key points are <math>(0, 0),~ (\frac{\pi}{2}, 1), ~ (\pi, 0), ~ (\frac{3\pi}{2}, 0),~ \text{and } (2\pi, 0).</math> |

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

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− | | | + | |We can read off the answers for (a) - (d): |

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− | | | + | |Amplitude: -1, period: <math>\frac{2\pi}{3}~</math>, phase shift: Left by <math>\frac{\pi}{2}~</math> and vertical shift up by 1. |

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Line 35: | Line 35: | ||

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

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− | | | + | |The five key points for the graph are <math>(-\frac{\pi}{6}, 1), (0, 0), (\frac{\pi}{6}, 1), (\frac{\pi}{3}, 2), (\frac{\pi}{2}, 1)</math> |

− | + | |} | |

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− | + | {| class="mw-collapsible mw-collapsed" style = "text-align:left;" | |

− | + | ! Step 3: | |

− | |||

− | |||

− | |||

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− | |- | ||

− | |||

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− | | | + | |Now plot the five key points and sketch a graph that looks like the <math>\sin</math> graph through those points. |

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

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− | | | + | |Amplitude: -1, period: <math>\frac{2\pi}{3}~</math>, phase shift: Left by <math>\frac{\pi}{2}~</math> and vertical shift up by 1. |

|- | |- | ||

− | |The | + | |The five key points for the graph are <math>(-\frac{\pi}{6}, 1), (0, 0), (\frac{\pi}{6}, 1), (\frac{\pi}{3}, 2), (\frac{\pi}{2}, 1)</math> |

|- | |- | ||

− | |[[File: | + | |[[File:5_Sample_Final_19.png]] |

|} | |} | ||

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

## Latest revision as of 18:22, 2 June 2015

**Question ** Consider the following function,

- a. What is the amplitude?
- b. What is the period?
- c. What is the phase shift?
- d. What is the vertical shift?
- e. Graph one cycle of f(x). Make sure to label five key points.

- a. What is the amplitude?

Foundations: |
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1) For parts (a) - (d), How do we read the relevant information off of |

2) What are the five key points when looking at |

Answer: |

1) The amplitude is A, the period is , the horizontal shift is left by C units if C is positive and right by C units if C is negative, the vertical shift is up by D if D is positive and down by D units if D is negative. |

2) The five key points are |

Solution:

Step 1: |
---|

We can read off the answers for (a) - (d): |

Amplitude: -1, period: , phase shift: Left by and vertical shift up by 1. |

Step 2: |
---|

The five key points for the graph are |

Step 3: |
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Now plot the five key points and sketch a graph that looks like the graph through those points. |

Final Answer: |
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Amplitude: -1, period: , phase shift: Left by and vertical shift up by 1. |

The five key points for the graph are |