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(π‘₯). A transformation maps 𝑓(π‘₯) to 𝑓(π‘₯)βˆ’3. Determine the coordinates of 𝐴 following this transformation.

  • A(48,1)
  • B(45,4)
  • C(42,1)
  • D(45,βˆ’2)
  • E(42,βˆ’2)

Q2:

The figure shows the graph of 𝑦=π‘₯sin.

Which of the following is a graph of 𝑦=2π‘₯sin?

  • A
  • B
  • C
  • D
  • E

Q3:

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

  • A𝑦=π‘₯cos
  • B𝑦=2π‘₯sin
  • C𝑦=π‘₯sin
  • D𝑦=2π‘₯sin
  • E𝑦=2π‘₯cos

Q4:

Which function is represented on the graph?

  • A𝑦=π‘₯cos
  • B𝑦=2π‘₯cos
  • C𝑦=2π‘₯sin

Q5:

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

  • A𝑦=2π‘₯sin
  • B𝑦=(π‘₯)+2sin
  • C𝑦=2π‘₯sin
  • D𝑦=(π‘₯)βˆ’2sin
  • E𝑦=(π‘₯βˆ’2)sin

Q6:

The figure shows the graph of 𝑓(π‘₯). A transformation maps 𝑓(π‘₯) to 𝑓(2π‘₯). Determine the coordinates of 𝐴 following this transformation.

  • A(22.5,0.5)
  • B(22.5,1)
  • C(90,1)
  • D(45,2)
  • E(45,0.5)

Q7:

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

  • A𝑦=2π‘₯sin
  • B𝑦=2π‘₯sin
  • C𝑦=π‘₯+2sin
  • D𝑦=(π‘₯βˆ’2)sin
  • E𝑦=(π‘₯+2)sin

Q8:

Which of the following is the graph of 𝑦=(π‘₯βˆ’90)cos?

  • A
  • B
  • C
  • D
  • E

Q9:

Which of the following is the graph of 𝑦=12(π‘₯βˆ’45)sin?

  • A
  • B
  • C
  • D
  • E

Q10:

Which of the following equations is represented by the given graph?

  • A𝑦=2π‘₯sin
  • B𝑦=2π‘₯sins
  • C𝑦=π‘₯+2sin
  • D𝑦=(π‘₯+2)sin
  • E𝑦=(π‘₯βˆ’2)sin

Q11:

Which of the following is the graph of 𝑦=(3π‘₯+90)sin?

  • A
  • B
  • C
  • D
  • E

Q12:

Which of the following is the graph of 𝑦=(π‘₯βˆ’90)sin?

  • A
  • B
  • C
  • D
  • E

Q13:

Which of the following is the graph of 𝑦=ο€»π‘₯4ο‡βˆ’1sin?

  • A
  • B
  • C
  • D
  • E

Q14:

Which of the following is the graph of 𝑦=(2π‘₯βˆ’90)cos?

  • A
  • B
  • C
  • D
  • E

Q15:

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

Q16:

The figure shows the graph of 𝑦=π‘₯sin.

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

  • A
  • B
  • C
  • D
  • E

Q17:

The figure shows the graph of 𝑦=π‘₯sin.

Which of the following is a graph of 𝑦=2π‘₯sin?

  • A
  • B
  • C
  • D
  • E

Q18:

The figure shows the graph of 𝑦=π‘₯sin.

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

  • A
  • B
  • C
  • D
  • E

Q19:

The figure shows the graph of a periodic function.

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

  • A
  • B
  • C
  • D

Q20:

The figure shows the graph of 𝑦=π‘₯sin.

Which of the following is a graph of 𝑦=(π‘₯)βˆ’2sin?

  • A
  • B
  • C
  • D
  • E

Q21:

Which of the following is the graph of 𝑦=212π‘₯cos?

  • A
  • B
  • C
  • D
  • E

Q22:

The figure shows the graph of a periodic function.

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

  • A
  • B
  • C
  • D

Q23:

The figure shows the graph of 𝑓(π‘₯). A transformation maps 𝑓(π‘₯) to βˆ’3𝑓(5π‘₯βˆ’5)βˆ’4. Determine the coordinates of 𝐴 following this transformation.

  • A(10,βˆ’3)
  • B(10,βˆ’7)
  • C(14,βˆ’7)
  • D(14,βˆ’4)
  • E(14,βˆ’3)

Q24:

The figure shows the graph of 𝑓(π‘₯). A transformation maps 𝑓(π‘₯) to βˆ’4𝑓(π‘₯). Determine the coordinates of 𝐴 following this transformation.

  • A(45,βˆ’0.25)
  • B(βˆ’180,βˆ’4)
  • C(βˆ’180,1)
  • D(45,βˆ’4)
  • E(βˆ’11.25,1)

Q25:

On the left is the graph of 𝑓(π‘₯) and on the right is the graph of 𝐴𝑓(π‘₯)+𝐡 for some numbers 𝐴 and 𝐡.

What is the pair (𝐴,𝐡)?

  • A(2,βˆ’3)
  • BThey cannot be determined.
  • C(0,3)
  • D(0,βˆ’3)
  • E(βˆ’2,3)

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