Lesson Worksheet: Transformation of Trigonometric Functions Mathematics • 10th Grade

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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 2𝑓(𝑥). Determine the coordinates of 𝐴 following this transformation.

  • A(180,−0.5)
  • B(90,−1)
  • C(180,−2)
  • D(360,−1)
  • E(360,−2)

Q2:

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

  • A(180,−3)
  • B(180,1)
  • C(178,−3)
  • D(182,−1)
  • E(178,−1)

Q3:

Which of the following is the graph of 𝑦=(𝑥−90)cos?

  • A
  • B
  • C
  • D
  • E

Q4:

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(180,−0.5)
  • B(90,−1)
  • C(90,−0.5)
  • D(180,−2)
  • E(360,−1)

Q5:

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

  • A(90, 2)
  • B(180, 1)
  • C(90, 0.5)
  • D(45, 0.5)
  • E(45, 1)

Q6:

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

  • A𝑦=2𝑥sin
  • B𝑦=(𝑥)+2sin
  • C𝑦=2𝑥sin
  • D𝑦=(𝑥)−2sin
  • E𝑦=(𝑥−2)sin

Q7:

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

  • A𝑦=(2𝑥)sin
  • B𝑦=(𝑥−2)sin
  • C𝑦=(𝑥)+2sin
  • D𝑦=2(𝑥)sin
  • E𝑦=(𝑥+2)sin

Q8:

Which of the following is the graph of 𝑦=(𝑥)+1cos?

  • A
  • B
  • C
  • D
  • E

Q9:

The figure shows the graph of 𝑓(𝑥). A transformation maps 𝑓(𝑥) to 4𝑓(3𝑥−45)+1. Determine the coordinates of 𝐴 following this transformation.

  • A(75,−3)
  • B(180,0)
  • C(75,−1)
  • D(105,−3)
  • E(75,−2)

Q10:

Which of the following is the graph of 𝑦=𝑥4−1sin?

  • A
  • B
  • C
  • D
  • E

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