Worksheet: Function Transformations: Dilation

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(𝑥3)?

  • A
  • B
  • C
  • D

Q2:

Which of the following graphs represents 𝑓(𝑥)=(𝑥1)?

  • 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.

  • A1,12
  • B(2,1)
  • C(2,2)
  • D2,12
  • 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).

  • A𝑔(𝑥)=12𝑓(2𝑥)
  • B𝑔(𝑥)=𝑓(2𝑥)
  • C𝑔(𝑥)=2𝑓(𝑥)
  • D𝑔(𝑥)=𝑓𝑥2
  • E𝑔(𝑥)=12𝑓(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)
  • C2,12
  • D(2,1)
  • E(4,2)

Q10:

The function 𝑦=𝑓(𝑥) is stretched in the vertical direction by a scale factor of 12. Write, in terms of 𝑓(𝑥), the equation of the transformed function.

  • A𝑦=𝑓(𝑥)2
  • B𝑦=2𝑓(𝑥)
  • C𝑦=𝑓(2𝑥)
  • D𝑦=𝑓(𝑥)+2
  • E𝑦=𝑓12𝑥

Q11:

The function 𝑦=𝑓(𝑥) is stretched in the horizontal direction by a scale factor of 2. Write, in terms of 𝑓(𝑥), the equation of the transformed function.

  • A𝑦=𝑓(2𝑥)
  • B𝑦=12𝑓(𝑥)
  • C𝑦=𝑓(𝑥+2)
  • D𝑦=2𝑓(𝑥)
  • E𝑦=𝑓𝑥2

Q12:

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(2𝑥).

  • A(1,1)
  • B(4,2)
  • C(2,1)
  • D(4,1)
  • E1,12

Q13:

The function 𝑦=𝑓(𝑥) is stretched in the vertical direction by a scale factor of 2. Write, in terms of 𝑓(𝑥), the equation of the transformed function.

  • A𝑦=12𝑓(𝑥)
  • B𝑦=𝑓(𝑥2)
  • C𝑔(𝑥)=12𝑓(2𝑥)
  • D𝑦=𝑓(2𝑥)
  • E𝑦=2𝑓(𝑥)

Q14:

The figure shows the graph of 𝑦=𝑓(𝑥).

Which of the following is the graph of 𝑦=12𝑓(𝑥)?

  • A
  • B
  • C
  • D
  • E

Q15:

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

  • A𝑔(𝑥)=𝑓(𝑥)2
  • B𝑔(𝑥)=𝑓𝑥2
  • C𝑔(𝑥)=2𝑓(𝑥)
  • D𝑔(𝑥)=12𝑓(2𝑥)

Q16:

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

  • A𝑔(𝑥)=𝑓(2𝑥)
  • B𝑔(𝑥)=12𝑓(𝑥)
  • C𝑔(𝑥)=2𝑓(𝑥)
  • D𝑔(𝑥)=𝑓𝑥2
  • E𝑔(𝑥)=12𝑓(2𝑥)

Q17:

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=𝑓𝑥2.

  • A(1,1)
  • B1,12
  • C(4,2)
  • D(4,1)
  • E(2,1)

Q18:

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

  • A𝑔(𝑥)=12𝑓(2𝑥)
  • B𝑔(𝑥)=12𝑓(𝑥)
  • C𝑔(𝑥)=𝑓𝑥2
  • D𝑔(𝑥)=𝑓(2𝑥)
  • E𝑔(𝑥)=2𝑓(𝑥)

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