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?

  • A𝑦=𝜋7
  • B𝑦=14
  • C𝑦=5
  • D𝑦=534
  • E𝑦=12

Q2:

What is the midline of 𝑦=𝑎𝑏(𝑥)+𝑘sin?

  • A𝑦=𝑘
  • B𝑦=𝑎
  • C𝑦=𝑏
  • D𝑦=𝑎+𝑘
  • E𝑦=2𝜋𝑏

Q3:

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

  • A𝑎
  • B𝑐
  • C2𝜋𝑏
  • D𝑏2𝜋
  • E𝑏

Q4:

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

  • A2𝜋𝑏
  • B
  • C𝑏2𝜋
  • D𝑏
  • E𝑎

Q5:

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

  • A𝑎𝑘
  • B𝑏
  • C𝑐
  • D𝑘𝑎
  • E𝑎

Q6:

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

  • A𝑓=𝑝+1
  • B𝑓𝑝=1
  • C𝑓=𝑝1
  • D𝑓𝑝=1
  • E𝑓𝑝=1

Q7:

What is the midline of 𝑓(𝑥)=𝑎(𝑏𝑥𝑐)+𝑘cos?

  • A𝑦=𝑎
  • B𝑦=𝑎+𝑘
  • C𝑦=𝑘
  • D𝑦=𝑐
  • E𝑦=𝑏

Q8:

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

  • A12𝜋
  • B2𝜋
  • C1𝜋
  • D3𝜋2
  • E𝜋

Q9:

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

  • A2𝜋
  • B𝜋2
  • C5
  • D32
  • E6

Q10:

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

  • A𝑏2𝜋
  • B𝑏
  • C𝑎
  • D
  • E2𝜋𝑏

Q11:

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

  • A10
  • B6
  • C𝜋2
  • D5
  • E32

Q12:

The figure shows a graph of a periodic function.

What is the amplitude of the function?

What is the midline of the function?

  • A𝑦=10
  • B𝑦=5
  • C𝑦=15
  • D𝑦=0
  • E𝑦=5

What is the period of the function?

What is the frequency of the function?

  • A120
  • B115
  • C15
  • D110
  • E123

What is the maximum value of the function?

What is the minimum value of the function?

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