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Worksheet: Period of a Cyclic Function

Q1:

Let be a periodic function. If is the smallest nonzero value for which for all , what do we call ?

  • Athe vertical shift of
  • Bthe horizontal shift of
  • Cthe period of
  • Dthe amplitude of
  • Ethe initial value of

Q2:

What is the definition of a periodic function for some nonzero constant ?

  • A for all
  • B for all
  • C for all
  • D for all
  • E for all

Q3:

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

  • A
  • B
  • C
  • D
  • E

Q4:

State if the following is true: If has period , then so . Therefore, also has a period .

  • Afalse
  • Btrue

Q5:

A function has a period . Among the following statements, which one is NOT necessarily true?

  • A
  • B
  • C
  • D

Q6:

A point is traveling on a unit circle at a speed of one complete rotation per second.

If its position represents an angle at a time , when will it have the same position again?

  • Atwo seconds later
  • Bone and a half seconds later
  • Cone second later
  • Dhalf a second later
  • Eone-third of a second later

How would you express the angle representing its position at this time?

  • A
  • B
  • C
  • D
  • E

Deduce what the period of the cosine and sine functions is.

  • A
  • B
  • C
  • D
  • E

Q7:

Consider the function .

Determine the amplitude.

  • Aamplitude
  • Bamplitude
  • Camplitude
  • Damplitude
  • Eamplitude

Determine the period.

  • Aperiod
  • Bperiod
  • Cperiod
  • Dperiod
  • Eperiod

Q8:

The figure shows the graph of .

Which of the following is a graph of ?

  • A
  • B
  • C
  • D
  • E

Q9:

Find the range and period of the function by drawing the function between 0 and .

  • Arange, period
  • Brange, period
  • Crange, period
  • Drange, period

Q10:

What is the period of the function ?

  • A
  • B
  • C
  • D
  • E

Q11:

What is the period of the function ?

  • A
  • B
  • C
  • D
  • E

Q12:

What is the period of the function ?

  • A
  • B
  • C
  • D
  • E

Q13:

What is the period of the function ?

  • A10
  • B6
  • C
  • D5
  • E

Q14:

What is the period of ?

  • A
  • B
  • C
  • D
  • E

Q15:

What is the period of ?

  • A
  • B
  • C
  • D
  • E

Q16:

Find the period of the function .

  • A
  • B
  • C
  • D

Q17:

What is the period of ?

  • A
  • B
  • C
  • D
  • E