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

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(π‘₯) and the blue graph has the equation 𝑦=𝑔(π‘₯). Express 𝑔(π‘₯) as a transformation of 𝑓(π‘₯).

  • A𝑔(π‘₯)=𝑓(π‘₯+3)
  • B𝑔(π‘₯)=𝑓(3π‘₯)
  • C𝑔(π‘₯)=𝑓(π‘₯)+3
  • D𝑔(π‘₯)=𝑓(π‘₯βˆ’3)
  • E𝑔(π‘₯)=𝑓(π‘₯)βˆ’3

Q2:

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

  • A𝑔(π‘₯)=𝑓(π‘₯)+2
  • B𝑔(π‘₯)=𝑓(π‘₯+2)
  • C𝑔(π‘₯)=𝑓(π‘₯)βˆ’2
  • D𝑔(π‘₯)=𝑓(2π‘₯)
  • E𝑔(π‘₯)=2𝑓(π‘₯)

Q3:

The figure shows the graph of 𝑦=𝑓(π‘₯).

Which of the following is the graph of 𝑦=𝑓(π‘₯+1)?

  • A
  • B
  • C
  • D
  • E

Q4:

The figure shows the graph of 𝑦=𝑓(π‘₯) and the point 𝐴. The point 𝐴 is a local maximum. Identify the corresponding local maximum for the transformation 𝑦=𝑓(π‘₯)βˆ’2.

  • A(2,3)
  • B(0,1)
  • C(4,1)
  • D(2,βˆ’2)
  • E(2,βˆ’1)

Q5:

The figure shows the graph of 𝑦=𝑓(π‘₯) and the point 𝐴. The point 𝐴 is a local maximum. Identify the corresponding local maximum for the transformation 𝑦=𝑓(π‘₯βˆ’1)+4.

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

Q6:

Graph (a) shows the curve 𝑦=π‘₯+2π‘₯, 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=π‘₯βˆ’3π‘₯+5π‘₯βˆ’7
  • B𝑦=π‘₯βˆ’3π‘₯+5π‘₯βˆ’5
  • C𝑦=π‘₯βˆ’3π‘₯+5π‘₯βˆ’3
  • D𝑦=π‘₯βˆ’3π‘₯+5π‘₯+1
  • E𝑦=π‘₯+3π‘₯+5π‘₯βˆ’5

Q7:

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

Q8:

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

  • A𝑦=𝑓(π‘₯)βˆ’4
  • B𝑦=4𝑓(π‘₯)
  • C𝑦=𝑓(4π‘₯)
  • D𝑦=𝑓(π‘₯+4)
  • E𝑦=𝑓(π‘₯)+4

Q9:

The function 𝑓(π‘₯)=(π‘₯βˆ’5)(π‘₯βˆ’2)(π‘₯+7) is translated +5 units in the direction of the positive π‘₯-axis. Find an equation for the transformed function.

  • A𝑓(π‘₯+5)=(π‘₯+1)(π‘₯+3)(π‘₯βˆ’12)
  • B𝑓(π‘₯βˆ’5)=(π‘₯βˆ’5)(π‘₯+5)
  • C𝑓(π‘₯+5)=(π‘₯+1)(π‘₯+3)(π‘₯+12)
  • D𝑓(π‘₯βˆ’5)=(π‘₯βˆ’10)(π‘₯βˆ’7)(π‘₯βˆ’2)
  • E𝑓(π‘₯βˆ’5)=(π‘₯βˆ’10)(π‘₯βˆ’7)(π‘₯+2)

Q10:

A function 𝑑(π‘₯) has π‘₯-intercepts at βˆ’4 and 9. Where are the intercepts of 𝑑(π‘₯βˆ’5)?

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

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