Lesson Worksheet: Function Transformations: Translations Mathematics • 10th Grade

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In this worksheet, we will practice identifying function transformations involving horizontal and vertical shifts.

Q1:

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

  • A𝑔(𝑥)=𝑓(𝑥+3)
  • B𝑔(𝑥)=𝑓(3𝑥)
  • C𝑔(𝑥)=𝑓(𝑥)+3
  • D𝑔(𝑥)=𝑓(𝑥−3)
  • E𝑔(𝑥)=𝑓(𝑥)−3

Q2:

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

  • A𝑔(𝑥)=𝑓(𝑥)+2
  • B𝑔(𝑥)=𝑓(𝑥+2)
  • C𝑔(𝑥)=𝑓(𝑥)−2
  • D𝑔(𝑥)=𝑓(2𝑥)
  • E𝑔(𝑥)=2𝑓(𝑥)

Q3:

The figure shows the graph of 𝑦=𝑓(𝑥).

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

  • A
  • B
  • C
  • D
  • E

Q4:

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(2,3)
  • B(0,1)
  • C(4,1)
  • D(2,−2)
  • E(2,−1)

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−1)+4.

  • A(3,5)
  • B(1,5)
  • C(−2,0)
  • D(−1,4)
  • E(6,0)

Q6:

Graph (a) shows the curve 𝑦=𝑥+2𝑥, which has a point of inflection at the origin. Determine the equation of graph (b), given that it is a translation of graph (a).

  • A𝑦=𝑥−3𝑥+5𝑥−7
  • B𝑦=𝑥−3𝑥+5𝑥−5
  • C𝑦=𝑥−3𝑥+5𝑥−3
  • D𝑦=𝑥−3𝑥+5𝑥+1
  • E𝑦=𝑥+3𝑥+5𝑥−5

Q7:

The function 𝑓(𝑥)=3𝑥+9 is translated +2 units in the 𝑦-direction and 𝑐 units in the 𝑥-direction to form the function 𝑔(𝑥)=3𝑥+2. Find the value of 𝑐.

Q8:

The graph of a function 𝑓, 𝑦=𝑓(𝑥), is translated four units in the positive 𝑦-direction. Write, in terms of 𝑓(𝑥), the equation of the translated graph.

  • A𝑦=𝑓(𝑥)−4
  • B𝑦=4𝑓(𝑥)
  • C𝑦=𝑓(4𝑥)
  • D𝑦=𝑓(𝑥+4)
  • E𝑦=𝑓(𝑥)+4

Q9:

The function 𝑓(𝑥)=(𝑥−5)(𝑥−2)(𝑥+7) is translated +5 units in the direction of the positive 𝑥-axis. Find an equation for the transformed function.

  • A𝑓(𝑥+5)=(𝑥+1)(𝑥+3)(𝑥−12)
  • B𝑓(𝑥−5)=(𝑥−5)(𝑥+5)
  • C𝑓(𝑥+5)=(𝑥+1)(𝑥+3)(𝑥+12)
  • D𝑓(𝑥−5)=(𝑥−10)(𝑥−7)(𝑥−2)
  • E𝑓(𝑥−5)=(𝑥−10)(𝑥−7)(𝑥+2)

Q10:

A function 𝑡(𝑥) has 𝑥-intercepts at −4 and 9. Where are the intercepts of 𝑡(𝑥−5)?

  • Aat −9 and 4
  • Bat 1 and 14
  • Cat 20 and −45
  • Dat −4 and 9

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