Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Lesson: Periodic Functions

Sample Question Videos

Worksheet • 21 Questions • 3 Videos

Q1:

Which function is represented on the graph?

  • A 𝑦 = π‘₯ s i n
  • B 𝑦 = π‘₯ c o s
  • C 𝑦 = 2 π‘₯ s i n

Q2:

What is the maximum value of the function 𝑓 ( π‘₯ ) = π‘Ž ( 𝑏 ( π‘₯ βˆ’ β„Ž ) ) + π‘˜ s i n ?

  • A π‘Ž + π‘˜
  • B β„Ž
  • C 2 πœ‹ 𝑏
  • D 𝑏
  • E π‘Ž

Q3:

What is the amplitude of the function 𝑓 ( π‘₯ ) = π‘Ž ( 𝑏 ( π‘₯ βˆ’ β„Ž ) ) + π‘˜ s i n ?

  • A π‘Ž
  • B β„Ž
  • C 2 πœ‹ 𝑏
  • D 𝑏
  • E π‘Ž + π‘˜

Q4:

Simplify c o s ( 1 8 0 βˆ’ πœƒ ) ∘ .

  • A βˆ’ πœƒ c o s
  • B c o s πœƒ
  • C βˆ’ πœƒ s i n
  • D s i n πœƒ

Q5:

What is the midline of 𝑦 = π‘₯ s i n ?

  • A 𝑦 = 0
  • B 𝑦 = πœ‹ 7 + 1 2
  • C 𝑦 = 5 4
  • D 𝑦 = πœ‹ 7
  • E 𝑦 = 5 3 4

Q6:

The figure shows the graph of 𝑦 = π‘₯ s i n .

Which of the following is a graph of 𝑦 = 2 π‘₯ s i n ?

  • A
  • B
  • C
  • D
  • E

Q7:

The figure shows the graph of 𝑦 = π‘₯ s i n .

Which of the following is a graph of 𝑦 = ( π‘₯ ) + 2 s i n ?

  • A
  • B
  • C
  • D
  • E

Q8:

Which of the plots shown in the graph represents the tangent function?

  • A the green plot
  • B the red plot
  • C the blue plot

Q9:

What is the amplitude of the function 𝑓 ( π‘₯ ) = π‘Ž ( 𝑏 π‘₯ βˆ’ 𝑐 ) + π‘˜ c o s ?

  • A π‘Ž
  • B 2 πœ‹ 𝑏
  • C 𝑏
  • D π‘Ž + π‘˜
  • E 𝑐

Q10:

Let 𝑓 ( π‘₯ ) = 2 π‘₯ s i n . What is the smallest positive value of 𝑃 for which 𝑓 ( π‘₯ + 𝑃 ) = 𝑓 ( π‘₯ ) holds?

  • A πœ‹
  • B 3 πœ‹ 2
  • C πœ‹ 2
  • D πœ‹ 3
  • E 2 πœ‹

Q11:

Simplify s i n ( 1 8 0 βˆ’ πœƒ ) ∘ .

  • A s i n πœƒ
  • B βˆ’ πœƒ s i n
  • C βˆ’ πœƒ c o s
  • D c o s πœƒ

Q12:

Simplify s i n ( 3 6 0 βˆ’ πœƒ ) ∘ .

  • A βˆ’ πœƒ s i n
  • B s i n πœƒ
  • C βˆ’ πœƒ c o s
  • D c o s πœƒ

Q13:

The figure shows the graph of a periodic function.

The height of the function’s midline was doubled. Which of the following is the graph of the resulting function?

  • A
  • B
  • C
  • D

Q14:

The figure shows the graph of 𝑦 = π‘₯ s i n .