Graphing with Phase Shift Homework



Graphing with Phase Shift Homework

Pre-Calculus – Section 5.6

Find the period and phase shift for the following functions.

|1. y = 9 sin (7x – 2) |2. y = ⅓ cos (½x + 11) |3. y = – tan (2πx + 3) |

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|Period: |Period: |Period: |

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|Phase Shift: |Phase Shift: |Phase Shift: |

|4. y = 4 cot (5x + 3π) |5. y = ⅝ sec (6x – π) |6. y = csc ([pic]x – [pic]) |

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|Period: |Period: |Period: |

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|Phase Shift: |Phase Shift: |Phase Shift: |

Graph each function using vertical stretch/compression, period, and phase shift. Label each axis, and state the domain and range.

|7. y = 2 sin (3x – π) |

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|Domain: |

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|Range: |

|8. y = -3 cos [pic] |

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|Domain: |

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|Range: |

Graph each function using vertical stretch/compression, period, and phase shift. Label each axis, and state the domain and range.

|9. y = 3 csc [pic] |

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|Domain: |

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|Range: |

|10. y = tan [pic] |

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|Domain: |

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|Range: |

|11. y = sin [pic] + 3 |

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|Domain: |

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|Range: |

Write the equation of the sine function that has the given characteristics.

|12. Amplitude: 5 |13. Amplitude: 4 |

|Period: π |Period: 3π |

|Phase Shift: ½ |Phase Shift: -2 |

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