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Lesson: Graphing Periodic Functions

Worksheet • 11 Questions

Q1:

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

  • A πœ‹ 2
  • B10
  • C 3 2
  • D6
  • E5

Q2:

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

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

Q3:

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

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

Q4:

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

  • A 2 πœ‹
  • B πœ‹ 2
  • C 3 2
  • D6
  • E5

Q5:

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

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

Q6:

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

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

Q7:

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

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

Q8:

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

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

Q9:

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

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

Q10:

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

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

Q11:

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

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