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 ๐‘ฆ = 5 4 ๏€ป ๐œ‹ ๐‘ฅ 7 โˆ’ 5 ๏‡ + 1 2 c o s ?

  • A ๐‘ฆ = 5
  • B ๐‘ฆ = 1 4
  • C ๐‘ฆ = ๐œ‹ 7
  • D ๐‘ฆ = 1 2
  • E ๐‘ฆ = 5 3 4

Q2:

What is the midline of ๐‘ฆ = ๐‘Ž ๐‘ ( ๐‘ฅ โˆ’ โ„Ž ) + ๐‘˜ s i n ?

  • A ๐‘ฆ = ๐‘Ž
  • B ๐‘ฆ = 2 ๐œ‹ ๐‘
  • C ๐‘ฆ = ๐‘Ž + ๐‘˜
  • D ๐‘ฆ = ๐‘˜
  • E ๐‘ฆ = ๐‘

Q3:

What is the frequency of the function ๐‘“ ( ๐‘ก ) = ๐‘Ž ( ๐‘ ๐‘ก โˆ’ ๐‘ ) + ๐‘˜ c o s ?

  • A ๐‘
  • B ๐‘Ž
  • C ๐‘
  • D ๐‘ 2 ๐œ‹
  • E 2 ๐œ‹ ๐‘

Q4:

What is the period of the function ๐‘“ ( ๐‘ฅ ) = ๐‘Ž ( ๐‘ ( ๐‘ฅ โˆ’ โ„Ž ) ) + ๐‘˜ s i n ?

  • A ๐‘
  • B ๐‘Ž
  • C โ„Ž
  • D 2 ๐œ‹ ๐‘
  • E ๐‘ 2 ๐œ‹

Q5:

What is the minimum value of the function ๐‘“ ( ๐‘ฅ ) = ๐‘Ž ( ๐‘ ๐‘ฅ โˆ’ ๐‘ ) + ๐‘˜ c o s ?

  • A ๐‘
  • B ๐‘Ž
  • C ๐‘
  • D ๐‘˜ โˆ’ ๐‘Ž
  • E ๐‘Ž โˆ’ ๐‘˜

Q6:

Which of the following relates the frequency ๐‘“ and the period ๐‘ of a trigonometric function?

  • A ๐‘“ = ๐‘ โˆ’ 1
  • B ๐‘“ ๐‘ = โˆ’ 1
  • C ๐‘“ ๐‘ = 1
  • D ๐‘“ ๐‘ = 1
  • E ๐‘“ = ๐‘ + 1

Q7:

What is the midline of ๐‘“ ( ๐‘ฅ ) = ๐‘Ž ( ๐‘ ๐‘ฅ โˆ’ ๐‘ ) + ๐‘˜ c o s ?

  • A ๐‘ฆ = ๐‘
  • B ๐‘ฆ = ๐‘Ž
  • C ๐‘ฆ = ๐‘
  • D ๐‘ฆ = ๐‘˜
  • E ๐‘ฆ = ๐‘Ž + ๐‘˜

Q8:

What is the frequency of the function ๐‘“ ( ๐‘ก ) = ๐‘ก s i n ?

  • A 2 ๐œ‹
  • B 1 ๐œ‹
  • C ๐œ‹
  • D 1 2 ๐œ‹
  • E 3 ๐œ‹ 2

Q9:

What is the frequency of the function ๐‘“ ( ๐‘ก ) = 5 ( 4 ๐‘ก + 6 ) + 1 0 s i n ?

  • A5
  • B 3 2
  • C6
  • D 2 ๐œ‹
  • E ๐œ‹ 2

Q10:

What is the frequency of the function ๐‘“ ( ๐‘ก ) = ๐‘Ž ( ๐‘ ( ๐‘ก โˆ’ โ„Ž ) ) + ๐‘˜ s i n ?

  • A ๐‘Ž
  • B 2 ๐œ‹ ๐‘
  • C ๐‘
  • D ๐‘ 2 ๐œ‹
  • E โ„Ž

Q11:

What is the period of the function ๐‘“ ( ๐‘ฅ ) = 5 ( 4 ๐‘ฅ + 6 ) + 1 0 s i n ?

  • A5
  • B 3 2
  • C6
  • D ๐œ‹ 2
  • E10

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