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Relate a function's graph to its inverse

12th grade (Year 13 in England) · 16 questions · Common Core: HSF.BF.B.4.C · England: A-level Pure Mathematics

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  1. Question 1

    The graph of y = f(x) passes through (−6, −2). Which transformation maps it onto the graph of y = f⁻¹(x)?

    • A. Reflection in the x-axis
    • B. Reflection in the line y = x
    • C. Rotation of 180° about the origin
    • D. Reflection in the line y = −x

  2. Question 2

    The point (4, −7) is on the graph of y = f(x). Which point must be on the graph of y = f⁻¹(x)? Type it like (2, −1).

    Answer

  3. Question 3

    f(x) = x³ − 9. Find f⁻¹(−1).

    Answer

  4. Question 4

    The graph of y = f(x) passes through (4, 5). Which transformation maps it onto the graph of y = f⁻¹(x)?

    • A. Reflection in the line y = −x
    • B. Reflection in the line y = x
    • C. Reflection in the y-axis
    • D. Reflection in the x-axis

  5. Question 5

    The point (−2, −1) is on the graph of y = f(x). Which point must be on the graph of y = f⁻¹(x)? Type it like (2, −1).

    Answer

  6. Question 6

    f(x) = x³ − 4. Find f⁻¹(−12).

    Answer

  7. Question 7

    The graph of y = f(x) passes through (−1, −3). Which transformation maps it onto the graph of y = f⁻¹(x)?

    • A. Reflection in the x-axis
    • B. Reflection in the line y = x
    • C. Reflection in the y-axis
    • D. Reflection in the line y = −x

  8. Question 8

    The point (−3, 8) is on the graph of y = f(x). Which point must be on the graph of y = f⁻¹(x)? Type it like (2, −1).

    Answer

  9. Question 9

    f(x) = x³ + 0. Find f⁻¹(1).

    Answer

  10. Question 10

    The graph of y = f(x) passes through (−3, −1). Which transformation maps it onto the graph of y = f⁻¹(x)?

    • A. Reflection in the line y = x
    • B. Reflection in the y-axis
    • C. Reflection in the line y = −x
    • D. Reflection in the x-axis

  11. Question 11

    The point (−8, −3) is on the graph of y = f(x). Which point must be on the graph of y = f⁻¹(x)? Type it like (2, −1).

    Answer

  12. Question 12

    f(x) = x³ − 9. Find f⁻¹(−10).

    Answer

  13. Question 13

    The graph of y = f(x) passes through (−5, 2). Which transformation maps it onto the graph of y = f⁻¹(x)?

    • A. Reflection in the line y = −x
    • B. Reflection in the line y = x
    • C. Rotation of 180° about the origin
    • D. Reflection in the y-axis

  14. Question 14

    The point (−8, −7) is on the graph of y = f(x). Which point must be on the graph of y = f⁻¹(x)? Type it like (2, −1).

    Answer

  15. Question 15

    f(x) = x³ + 8. Find f⁻¹(8).

    Answer

  16. Question 16

    The graph of y = f(x) passes through (6, 0). Which transformation maps it onto the graph of y = f⁻¹(x)?

    • A. Reflection in the y-axis
    • B. Reflection in the line y = x
    • C. Rotation of 180° about the origin
    • D. Reflection in the x-axis

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  1. Reflection in the line y = x
  2. (−7, 4)
  3. 2
  4. Reflection in the line y = x
  5. (−1, −2)
  6. -2
  7. Reflection in the line y = x
  8. (8, −3)
  9. 1
  10. Reflection in the line y = x
  11. (−3, −8)
  12. -1
  13. Reflection in the line y = x
  14. (−7, −8)
  15. 0
  16. Reflection in the line y = x