Lesson Worksheet: Graphing Periodic Functions Mathematics • 10th Grade

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

Q1:

What is the midline of 𝑦=54ο€»πœ‹π‘₯7βˆ’5+12cos?

  • A𝑦=πœ‹7
  • B𝑦=14
  • C𝑦=5
  • D𝑦=534
  • E𝑦=12

Q2:

What is the midline of 𝑦=π‘Žπ‘(π‘₯βˆ’β„Ž)+π‘˜sin?

  • A𝑦=π‘˜
  • B𝑦=π‘Ž
  • C𝑦=𝑏
  • D𝑦=π‘Ž+π‘˜
  • E𝑦=2πœ‹π‘

Q3:

What is the frequency of the function 𝑓(𝑑)=π‘Ž(π‘π‘‘βˆ’π‘)+π‘˜cos?

  • Aπ‘Ž
  • B𝑐
  • C2πœ‹π‘
  • D𝑏2πœ‹
  • E𝑏

Q4:

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

  • A2πœ‹π‘
  • Bβ„Ž
  • C𝑏2πœ‹
  • D𝑏
  • Eπ‘Ž

Q5:

What is the minimum value of the function 𝑓(π‘₯)=π‘Ž(𝑏π‘₯βˆ’π‘)+π‘˜cos?

  • Aπ‘Žβˆ’π‘˜
  • B𝑏
  • C𝑐
  • Dπ‘˜βˆ’π‘Ž
  • Eπ‘Ž

Q6:

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

  • A𝑓=𝑝+1
  • B𝑓𝑝=1
  • C𝑓=π‘βˆ’1
  • D𝑓𝑝=1
  • E𝑓𝑝=βˆ’1

Q7:

What is the midline of 𝑓(π‘₯)=π‘Ž(𝑏π‘₯βˆ’π‘)+π‘˜cos?

  • A𝑦=π‘Ž
  • B𝑦=π‘Ž+π‘˜
  • C𝑦=π‘˜
  • D𝑦=𝑐
  • E𝑦=𝑏

Q8:

What is the frequency of the function 𝑓(𝑑)=𝑑sin?

  • A12πœ‹
  • B2πœ‹
  • C1πœ‹
  • D3πœ‹2
  • Eπœ‹

Q9:

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

  • A2πœ‹
  • Bπœ‹2
  • C5
  • D32
  • E6

Q10:

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

  • A𝑏2πœ‹
  • B𝑏
  • Cπ‘Ž
  • Dβ„Ž
  • E2πœ‹π‘

This lesson includes 2 additional questions for subscribers.

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