Lesson Worksheet: Graphs of Inverses of Functions Mathematics • 10th Grade

In this worksheet, we will practice using a graph to find the inverse of a function and analyzing the graphs for the inverse of a function.

Q1:

If we drew the function 𝑓(π‘₯) and its inverse function 𝑓(π‘₯) on the same graph, which of the following must be true?

  • AThere would be symmetry about the line 𝑦=π‘₯.
  • BThere would be symmetry about the π‘₯-axis.
  • CThere would be symmetry about the origin.
  • DThere would be symmetry about the 𝑦-axis.
  • EThe two graphs would be the same.

Q2:

The following is the graph of 𝑓(π‘₯)=2π‘₯βˆ’1.

Which of the following is the graph of the inverse function 𝑓(π‘₯)?

  • A(b)
  • B(a)
  • C(c)
  • D(d)

Q3:

In the given figure, the green points represent the function 𝑓(π‘₯). Do the blue points represent 𝑓(π‘₯)?

  • ANo
  • BYes

Q4:

Which of the following Graphs represents a function 𝑓(π‘₯) and its inverse function 𝑓(π‘₯)?

  • Ad
  • Bb
  • Cc
  • Da

Q5:

By sketching the graphs of the following functions, which is the inverse of itself?

  • A1π‘₯
  • Bπ‘₯
  • Cπ‘₯
  • D1π‘₯

Q6:

By sketching the graphs of 𝑓(π‘₯)=2π‘₯ and 𝑔(π‘₯)=ο„žπ‘₯2 for π‘₯β‰₯0, determine whether they are inverse functions.

  • AThey are not inverse functions.
  • BThey are inverse functions.

Q7:

The graph of 𝑓(π‘₯)=4π‘₯βˆ’7 is shown. Which of the points 𝐴(2,3), 𝐡(βˆ’2,2), 𝐢(1,2), and 𝐷(1,3) lies on the graph of the inverse function 𝑓(π‘₯)?

  • A𝐡
  • B𝐢
  • C𝐴
  • D𝐷

Q8:

The graph of 𝑓(π‘₯)=(π‘₯βˆ’2)+3 for the interval [2,∞) is shown. Which of the points 𝐴(3,1), 𝐡(7,4), 𝐢(9,5), and 𝐷(4,βˆ’2) lies on the graph of its inverse function 𝑓(π‘₯)?

  • A𝐡
  • B𝐴
  • C𝐢
  • D𝐷

Q9:

Shown is the graph of 𝑓(π‘₯)=5π‘₯+6. Find the intersection of the inverse function 𝑓(π‘₯) with the π‘₯-axis.

  • Aο€Όβˆ’65,0
  • Bο€Ό56,0
  • C(βˆ’6,0)
  • Dο€Ό65,0
  • E(6,0)

Q10:

The graphs of 𝑓(π‘₯)=π‘₯+π‘οŠ© and its inverse 𝑓(π‘₯) intersect at three points, one of which is ο€Ό45,45.

Determine the value of 𝑏.

  • A64125
  • B45
  • C36125
  • D164125
  • Eβˆ’45

Find the π‘₯-coordinate of the point 𝐴 marked on the figure.

  • A45
  • B164125
  • Cβˆ’45
  • D36125
  • E64125

Find the π‘₯-coordinate of the point 𝐡 marked on the figure.

  • Aβˆ’2βˆ’βˆš135
  • B825
  • C36125
  • D13
  • E√13βˆ’25

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