Worksheet: Transformation of Trigonometric Functions

In this worksheet, we will practice translating or stretching the trigonometric function and finding the rule of a trigonometric function given the transformation.

Q1:

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

Q2:

The figure shows the graph of 𝑦=𝑥sin.

Which of the following is a graph of 𝑦=2𝑥sin?

  • A
  • B
  • C
  • D
  • E

Q3:

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

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

Q4:

Which function is represented on the graph?

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

Q5:

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

Q6:

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

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

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:

Which of the following is the graph of 𝑦=(𝑥90)cos?

  • A
  • B
  • C
  • D
  • E

Q9:

Which of the following is the graph of 𝑦=12(𝑥45)sin?

  • A
  • B