TRANSFORMATIONS of Trigonometric Functions



MultipleTRANSFORMATIONS of Trigonometric Functions(1)

Date: ______________________

Graph each function. State amplitude, period, phase shift & vertical translation.

1. [pic]

Amplitude (AMP)= _____

Period Length(PL)= _____

Phase Shift (PS)= _____

Vertical Shift(VS) = _____

2. [pic]

Amplitude (AMP)= _____

Period Length(PL)= _____

Phase Shift (PS)= _____

Vertical Shift(VS) = _____

3. [pic]

Amplitude (AMP)= _____

Period Length(PL)= _____

Phase Shift (PS)= _____

Vertical Shift(VS) = _____

4. [pic]

Amplitude (AMP)= _____

Period Length(PL)= _____

Phase Shift (PS)= _____

Vertical Shift(VS) = _____

Math Work

1. For each of the following state the amplitude,period,phase shift and vertical translation

a) [pic] b) [pic] c) [pic]d) [pic]

e) [pic]

2. For each of the following graphs of a sine function, state the following:

i) the amplitude ii) the period iii) phase shift iv) vertical translation

v) equation of sinusoidal or median axis vi) minimum value and when it occurs

vii) maximum value and when it occurs viii) equation of the graph

2. a) b)

d)

3. For each graph in number 2, write an equation that represents it as a cosine function.

4. For each graph of the following functions:

i) determine the amplitude, phase shift, period and vertical translation

ii) graph

iii) state the domain and range

4a) [pic] b)[pic]c) [pic] d) [pic]

5. For each of the following functions graph them and determine the maximum and minimums.

5. a)[pic] b) [pic] c) [pic] d) [pic]

e) [pic]

Answers:

|1. |AMP |PL |PS |VS |2. |i |

|a) |5 |none |[pic] |Up 3 |[pic] |[pic] |

|b) |2 |right[pic] |[pic] |none |[pic] |[pic] |

|c) |3 |Right [pic] | [pic] |Down 5 |[pic] |[pic] |

|d) |1 |Right [pic] |[pic] |Up 2 |[pic] |[pic] |

|5. |Max points |Min points | |Max points | |Min Points |

|a) |[pic] |[pic] |b) |[pic] | |[pic] |

|c) |[pic] |[pic] |d) |[pic] | |[pic] |

Graphs #4,5 shown next day

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