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

In this worksheet, we will practice reflecting a graph on the x- or y-axis, both graphically and algebraically.

Q1:

Which of the following processes would you use to obtain the graph of 𝑦=βˆ’π‘“(βˆ’π‘₯) from the graph of 𝑦=𝑓(π‘₯)?

  1. reflect the graph in the π‘₯-axis
  2. reflect the graph in the 𝑦-axis
  3. reflect the graph in the line 𝑦=π‘₯
  4. reflect the graph in the line 𝑦=βˆ’π‘₯
  • Aa only
  • Bd only
  • Cb only
  • Dc and d
  • Ea and b

Q2:

Find 𝑔(π‘₯), where the graph of the function 𝑔(π‘₯) is a reflection across π‘₯-axis of the graph of the function 𝑓(π‘₯)=2π‘₯+5.

  • A𝑔(π‘₯)=2π‘₯βˆ’5
  • B𝑔(π‘₯)=βˆ’2π‘₯βˆ’5
  • C𝑔(π‘₯)=2π‘₯βˆ’7
  • D𝑔(π‘₯)=2π‘₯+5
  • E𝑔(π‘₯)=βˆ’2π‘₯+5

Q3:

This is the graph of 𝑦=𝑔(π‘₯).

Which of the following is the graph of 𝑔(βˆ’π‘₯)?

  • A(c)
  • B(b)
  • C(a)

Q4:

The following linear graph represents a function 𝑔(π‘₯) after a reflection on the 𝑦-axis. Find the original function 𝑓(π‘₯).

  • A𝑓(π‘₯)=βˆ’2π‘₯βˆ’4
  • B𝑓(π‘₯)=2π‘₯βˆ’4
  • C𝑓(π‘₯)=2π‘₯+4
  • D𝑓(π‘₯)=βˆ’2π‘₯+4

Q5:

The graph of the function 𝑓(π‘₯)=2π‘₯log is reflected symmetrically over the 𝑦-axis to obtain the graph of the function 𝑔(π‘₯). Which of the following is the graph of the function 𝑔(π‘₯)?

  • A
  • B
  • C
  • D
  • E

Q6:

Graphs 𝐴 and 𝐡 in the diagram are the graphs of square root functions. They are symmetric about the origin. The equation of graph 𝐴 is 𝑦=13√π‘₯+2+1. Knowing that a point reflection about the origin is equivalent to a reflection in the π‘₯-axis followed by a reflection in the 𝑦-axis, find the equation of graph 𝐡.

  • A𝑦=βˆ’13βˆšβˆ’π‘₯+2βˆ’1
  • B𝑦=13βˆšβˆ’π‘₯+2βˆ’1
  • C𝑦=βˆ’13√π‘₯βˆ’2βˆ’1
  • D𝑦=βˆ’13βˆšβˆ’π‘₯βˆ’2βˆ’1
  • E𝑦=βˆ’13√π‘₯+2βˆ’1

Q7:

Consider the function 𝑓(π‘₯)=(π‘₯βˆ’1)+2, where π‘₯∈[1,∞).

Which of the graphs shown represents the function 𝑓(π‘₯)?

  • AB
  • BD
  • CA
  • DE
  • EC

Which of the graphs shown represents the reflection of 𝑓(π‘₯) on the π‘₯-axis?

  • AE
  • BC
  • CA
  • DD
  • EB

Which of the graphs shown represents the reflection of 𝑓(π‘₯) on the 𝑦-axis?

  • AA
  • BB
  • CC
  • DD
  • EE

Q8:

Consider the following table of the function 𝑓(π‘₯).

π‘₯1234
𝑓(π‘₯)1234

Choose the table of the reflected function 𝑔(π‘₯) over the 𝑦-axis.

  • A
    π‘₯βˆ’1βˆ’2βˆ’3βˆ’4
    𝑔(π‘₯)1234
  • B
    π‘₯1234
    𝑔(π‘₯)1234
  • C
    π‘₯1234
    𝑔(π‘₯)βˆ’1βˆ’2βˆ’3βˆ’4
  • D
    π‘₯βˆ’1βˆ’2βˆ’3βˆ’4
    𝑔(π‘₯)βˆ’1βˆ’2βˆ’3βˆ’4
  • E
    π‘₯1βˆ’234
    𝑔(π‘₯)1βˆ’234

Q9:

The following parabolic graph represents a function 𝑔(π‘₯) after a reflection on the π‘₯-axis. Find the original function 𝑓(π‘₯).

  • A𝑓(π‘₯)=(π‘₯+1)βˆ’5
  • B𝑓(π‘₯)=(π‘₯βˆ’1)+5
  • C𝑓(π‘₯)=βˆ’(π‘₯+1)+5
  • D𝑓(π‘₯)=(π‘₯+1)+5
  • E𝑓(π‘₯)=(π‘₯βˆ’1)βˆ’5

Q10:

Given the function 𝑓(π‘₯)=|π‘₯+3|+5, which of the following graphs is the reflection of 𝑓(π‘₯) on the 𝑦-axis?

  • A
  • B
  • C
  • D
  • E

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