Worksheet: Graphing Periodic Functions

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

Q1:

What is the midline of 𝑦=54𝜋𝑥75+12cos?

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

Q2:

What is the midline of 𝑦=𝑎𝑏(𝑥)+𝑘sin?

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

Q3:

What is the frequency of the function 𝑓(𝑡)=𝑎(𝑏𝑡𝑐)+𝑘cos?

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

Q4:

What is the period of the function 𝑓(𝑥)=𝑎(𝑏(𝑥))+𝑘sin?

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

Q5:

What is the minimum value of the function 𝑓(𝑥)=𝑎(𝑏𝑥𝑐)+𝑘cos?

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

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(𝑏𝑥𝑐)+𝑘cos?

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

Q8:

What is the frequency of the function 𝑓(𝑡)=𝑡sin?

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

Q9:

What is the frequency of the function 𝑓(𝑡)=5(4𝑡+6)+10sin?

  • A 2 𝜋
  • B 𝜋 2
  • C5
  • D 3 2
  • E6

Q10:

What is the frequency of the function 𝑓(𝑡)=𝑎(𝑏(𝑡))+𝑘sin?

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

Q11:

What is the period of the function 𝑓(𝑥)=5(4𝑥+6)+10sin?

  • A10
  • B6
  • C 𝜋 2
  • D5
  • E 3 2

Q12:

The figure shows a graph of a periodic function.

What is the amplitude of the function?

What is the midline of the function?

  • A 𝑦 = 1 0
  • B 𝑦 = 5
  • C 𝑦 = 1 5
  • D 𝑦 = 0
  • E 𝑦 = 5

What is the period of the function?

What is the frequency of the function?

  • A 1 2 0
  • B 1 1 5
  • C 1 5
  • D 1 1 0
  • E 1 2 3

What is the maximum value of the function?

What is the minimum value of the function?

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