Worksheet: Transformation of Periodic Functions

In this worksheet, we will practice finding the rule of a function whose graph is of a sine or cosine function that has been stretched in the x-direction or y-direction.

Q1:

Which function is represented on the graph?

  • A 𝑦 = 2 𝑥 s i n
  • B 𝑦 = 𝑥 c o s
  • C 𝑦 = 𝑥 s i n

Q2:

The figure shows the graph of 𝑓 ( 𝑥 ) . A transformation maps 𝑓 ( 𝑥 ) to 𝑓 ( 𝑥 ) 3 . Determine the coordinates of 𝐴 following this transformation.

  • A ( 4 2 , 2 )
  • B ( 4 5 , 4 )
  • C ( 4 8 , 1 )
  • D ( 4 5 , 2 )
  • E ( 4 2 , 1 )

Q3:

The figure shows the graph of 𝑦 = 𝑥 s i n .

Which of the following is a graph of 𝑦 = 2 𝑥 s i n ?

  • A
  • B
  • C
  • D
  • E

Q4:

Write the equation of the trigonometric function seen in the given figure.

  • A 𝑦 = 2 𝑥 c o s
  • B 𝑦 = 𝑥 c o s
  • C 𝑦 = 𝑥 s i n
  • D 𝑦 = 2 𝑥 s i n
  • E 𝑦 = 2 𝑥 s i n

Q5:

Which function is represented on the graph?

  • A 𝑦 = 2 𝑥 s i n
  • B 𝑦 = 𝑥 c o s
  • C 𝑦 = 2 𝑥 c o s

Q6:

Which of the following is the graph of 𝑦 = 𝑥 c o s ?

  • A
  • B
  • C
  • D
  • E

Q7:

The figure shows the graph of a function. Which of the following equations represents the graph?

  • A 𝑦 = 2 𝑥 s i n
  • B 𝑦 = 2 𝑥 s i n
  • C 𝑦 = ( 𝑥 ) + 2 s i n
  • D 𝑦 = ( 𝑥 2 ) s i n
  • E 𝑦 = ( 𝑥 ) 2 s i n

Q8:

The figure shows the graph of 𝑓 ( 𝑥 ) . A transformation maps 𝑓 ( 𝑥 ) to 𝑓 ( 2 𝑥 ) . Determine the coordinates of 𝐴 following this transformation.

  • A ( 4 5 , 2 )
  • B ( 9 0 , 1 )
  • C ( 4 5 , 0 . 5 )
  • D ( 2 2 . 5 , 1 )
  • E ( 2 2 . 5 , 0 . 5 )

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