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Worksheet: Graphing Periodic Functions

Q1:

What is the period of the function 𝑓 ( π‘₯ ) = 5 ( 4 π‘₯ + 6 ) + 1 0 s i n ?

  • A5
  • B 3 2
  • C6
  • D πœ‹ 2
  • E10

Q2:

What is the midline of 𝑦 = π‘Ž 𝑏 ( π‘₯ βˆ’ β„Ž ) + π‘˜ s i n ?

  • A 𝑦 = π‘Ž
  • B 𝑦 = 2 πœ‹ 𝑏
  • C 𝑦 = π‘Ž + π‘˜
  • D 𝑦 = π‘˜
  • E 𝑦 = 𝑏

Q3:

What is the frequency of the function 𝑓 ( 𝑑 ) = π‘Ž ( 𝑏 𝑑 βˆ’ 𝑐 ) + π‘˜ c o s ?

  • A 𝑏
  • B π‘Ž
  • C 𝑐
  • D 𝑏 2 πœ‹
  • E 2 πœ‹ 𝑏

Q4:

What is the frequency of the function 𝑓 ( 𝑑 ) = 5 ( 4 𝑑 + 6 ) + 1 0 s i n ?

  • A5
  • B 3 2
  • C6
  • D 2 πœ‹
  • E πœ‹ 2

Q5:

What is the frequency of the function 𝑓 ( 𝑑 ) = π‘Ž ( 𝑏 ( 𝑑 βˆ’ β„Ž ) ) + π‘˜ s i n ?

  • A π‘Ž
  • B 2 πœ‹ 𝑏
  • C 𝑏
  • D 𝑏 2 πœ‹
  • E β„Ž

Q6:

What is the frequency of the function 𝑓 ( 𝑑 ) = 𝑑 s i n ?

  • A 2 πœ‹
  • B 1 πœ‹
  • C πœ‹
  • D 1 2 πœ‹
  • E 3 πœ‹ 2

Q7:

What is the midline of 𝑓 ( π‘₯ ) = π‘Ž ( 𝑏 π‘₯ βˆ’ 𝑐 ) + π‘˜ c o s ?

  • A 𝑦 = 𝑏
  • B 𝑦 = π‘Ž
  • C 𝑦 = 𝑐
  • D 𝑦 = π‘˜
  • E 𝑦 = π‘Ž + π‘˜

Q8:

What is the period of the function 𝑓 ( π‘₯ ) = π‘Ž ( 𝑏 ( π‘₯ βˆ’ β„Ž ) ) + π‘˜ s i n ?

  • A 𝑏
  • B π‘Ž
  • C β„Ž
  • D 2 πœ‹ 𝑏
  • E 𝑏 2 πœ‹

Q9:

What is the minimum value of the function 𝑓 ( π‘₯ ) = π‘Ž ( 𝑏 π‘₯ βˆ’ 𝑐 ) + π‘˜ c o s ?

  • A 𝑏
  • B π‘Ž
  • C 𝑐
  • D π‘˜ βˆ’ π‘Ž
  • E π‘Ž βˆ’ π‘˜

Q10:

Which of the following relates the frequency 𝑓 and the period 𝑝 of a trigonometric function?

  • A 𝑓 = 𝑝 βˆ’ 1
  • B 𝑓 𝑝 = βˆ’ 1
  • C 𝑓 𝑝 = 1
  • D 𝑓 𝑝 = 1
  • E 𝑓 = 𝑝 + 1

Q11:

What is the midline of 𝑦 = 5 4 ο€» πœ‹ π‘₯ 7 βˆ’ 5  + 1 2 c o s ?

  • A 𝑦 = 5
  • B 𝑦 = 1 4
  • C 𝑦 = πœ‹ 7
  • D 𝑦 = 1 2
  • E 𝑦 = 5 3 4