Worksheet: Graphing Periodic Functions

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In this worksheet, we will practice graphing periodic functions and using key terminology, including frequency, period, amplitude.

Q1:

What is the midline of 𝑦 = 5 4 𝜋 𝑥 7 − 5 + 1 2 c o s ?

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

Q2:

What is the midline of 𝑦 = 𝑎 𝑏 ( 𝑥 − ℎ ) + 𝑘 s i n ?

  • A 𝑦 = 𝑎
  • B 𝑦 = 2 𝜋 𝑏
  • C 𝑦 = 𝑎 + 𝑘
  • D 𝑦 = 𝑘
  • E 𝑦 = 𝑏

Q3:

What is the frequency of the function 𝑓 ( 𝑡 ) = 𝑎 ( 𝑏 𝑡 − 𝑐 ) + 𝑘 c o s ?

  • A 𝑏
  • B 𝑎
  • C 𝑐
  • D 𝑏 2 𝜋
  • E 2 𝜋 𝑏

Q4:

What is the period of the function 𝑓 ( 𝑥 ) = 𝑎 ( 𝑏 ( 𝑥 − ℎ ) ) + 𝑘 s i n ?

  • A 𝑏
  • B 𝑎
  • C ℎ
  • D 2 𝜋 𝑏
  • E 𝑏 2 𝜋

Q5:

What is the minimum value of the function 𝑓 ( 𝑥 ) = 𝑎 ( 𝑏 𝑥 − 𝑐 ) + 𝑘 c o s ?

  • A 𝑏
  • B 𝑎
  • C 𝑐
  • D 𝑘 − 𝑎
  • E 𝑎 − 𝑘

Q6:

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 = 1
  • D 𝑓 𝑝 = 1
  • E 𝑓 = 𝑝 + 1

Q7:

What is the midline of 𝑓 ( 𝑥 ) = 𝑎 ( 𝑏 𝑥 − 𝑐 ) + 𝑘 c o s ?

  • A 𝑦 = 𝑏
  • B 𝑦 = 𝑎
  • C 𝑦 = 𝑐
  • D 𝑦 = 𝑘
  • E 𝑦 = 𝑎 + 𝑘

Q8:

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

  • A 2 𝜋
  • B 1 𝜋
  • C 𝜋
  • D 1 2 𝜋
  • E 3 𝜋 2

Q9:

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

  • A5
  • B 3 2
  • C6
  • D 2 𝜋
  • E 𝜋 2

Q10:

What is the frequency of the function 𝑓 ( 𝑡 ) = 𝑎 ( 𝑏 ( 𝑡 − ℎ ) ) + 𝑘 s i n ?

  • A 𝑎
  • B 2 𝜋 𝑏
  • C 𝑏
  • D 𝑏 2 𝜋
  • E ℎ

Q11:

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

  • A5
  • B 3 2
  • C6
  • D 𝜋 2
  • E10

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