Worksheet: Function Transformations: Dilation

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In this worksheet, we will practice identifying function transformations involving horizontal and vertical stretches or compressions.

Q1:

Given the graph of 𝑦=𝑔(𝑥), which of the following is the graph of 𝑦=𝑔(𝑥−3)?

  • A
  • B
  • C
  • D

Q2:

Which of the following graphs represents 𝑓(𝑥)=(𝑥−1)?

  • A(c)
  • B(b)
  • C(a)
  • D(d)

Q3:

Which of the following graphs represents 𝑓(𝑥)=(𝑥+3)?

  • A(a)
  • B(c)
  • C(b)
  • D(d)

Q4:

The figure shows the graph of 𝑦=𝑓(𝑥).

Which of the following is the graph of 𝑦=𝑓(2𝑥)?

  • A
  • B
  • C
  • D
  • E

Q5:

The figure shows the graph of 𝑦=𝑓(𝑥) and the point 𝐴. The point 𝐴 is a local maximum. Identify the corresponding local maximum for the transformation 𝑦=𝑓(𝑥)2.

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

Q6:

The figure shows the graph of 𝑦=𝑓(𝑥).

Which of the following is the graph of 𝑦=2𝑓(𝑥)?

  • A
  • B
  • C
  • D
  • E

Q7:

The figure shows the graph of 𝑦=𝑓(𝑥).

Which of the following is the graph of 𝑦=𝑓𝑥2?

  • A
  • B
  • C
  • D
  • E

Q8:

The red graph in the figure represents the equation 𝑦=𝑓(𝑥) and the blue graph represents the equation 𝑦=𝑔(𝑥). Express 𝑔(𝑥) as a transformation of 𝑓(𝑥).

  • A 𝑔 ( 𝑥 ) = 1 2 𝑓 ( 2 𝑥 )
  • B 𝑔 ( 𝑥 ) = 𝑓 ( 2 𝑥 )
  • C 𝑔 ( 𝑥 ) = 2 𝑓 ( 𝑥 )
  • D 𝑔 ( 𝑥 ) = 𝑓 𝑥 2
  • E 𝑔 ( 𝑥 ) = 1 2 𝑓 ( 𝑥 )

Q9:

The figure shows the graph of 𝑦=𝑓(𝑥) and the point 𝐴. The point 𝐴 is a local maximum. Identify the corresponding local maximum for the transformation 𝑦=2𝑓(𝑥).

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

Q10:

The function