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Transformations of functions

11th grade (Year 12 in England) · 16 questions · Common Core: HSF.BF.B.3 · England: GCSE Higher Algebra

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Score/ 16

  1. Question 1

    The graph of y = x² is transformed to y = (x + 2)² − 3. Where is the new vertex? Type it like (2, −1).

    xy−10−8−6−4−2246810−10−8−6−4−22468100O

    Answer

  2. Question 2

    Which transformation maps y = f(x) to y = −f(x)?

    • A. translate up 2
    • B. translate left 2
    • C. reflect in the x-axis
    • D. reflect in the y-axis

  3. Question 3

    The graph of y = x² is transformed to y = (x + 6)² − 2. Where is the new vertex? Type it like (2, −1).

    xy−10−8−6−4−2246810−10−8−6−4−22468100O

    Answer

  4. Question 4

    Which transformation maps y = f(x) to y = −f(x)?

    • A. translate up 3
    • B. translate left 3
    • C. reflect in the x-axis
    • D. reflect in the y-axis

  5. Question 5

    The graph of y = x² is transformed to y = (x − 2)² − 1. Where is the new vertex? Type it like (2, −1).

    xy−10−8−6−4−2246810−10−8−6−4−22468100O

    Answer

  6. Question 6

    Which transformation maps y = f(x) to y = f(x + 4)?

    • A. translate up 4
    • B. translate left 4
    • C. reflect in the x-axis
    • D. reflect in the y-axis

  7. Question 7

    The graph of y = x² is transformed to y = (x − 2)² + 6. Where is the new vertex? Type it like (2, −1).

    xy−10−8−6−4−2246810−10−8−6−4−22468100O

    Answer

  8. Question 8

    Which transformation maps y = f(x) to y = f(−x)?

    • A. translate up 4
    • B. translate left 4
    • C. reflect in the x-axis
    • D. reflect in the y-axis

  9. Question 9

    The graph of y = x² is transformed to y = (x + 5)² − 3. Where is the new vertex? Type it like (2, −1).

    xy−10−8−6−4−2246810−10−8−6−4−22468100O

    Answer

  10. Question 10

    Which transformation maps y = f(x) to y = f(x + 4)?

    • A. translate up 4
    • B. translate left 4
    • C. reflect in the x-axis
    • D. reflect in the y-axis

  11. Question 11

    The graph of y = x² is transformed to y = (x − 3)² − 1. Where is the new vertex? Type it like (2, −1).

    xy−10−8−6−4−2246810−10−8−6−4−22468100O

    Answer

  12. Question 12

    Which transformation maps y = f(x) to y = −f(x)?

    • A. translate up 3
    • B. translate left 3
    • C. reflect in the x-axis
    • D. reflect in the y-axis

  13. Question 13

    The graph of y = x² is transformed to y = (x + 2)² + 6. Where is the new vertex? Type it like (2, −1).

    xy−10−8−6−4−2246810−10−8−6−4−22468100O

    Answer

  14. Question 14

    Which transformation maps y = f(x) to y = f(x) + 2?

    • A. translate up 2
    • B. translate left 2
    • C. reflect in the x-axis
    • D. reflect in the y-axis

  15. Question 15

    The graph of y = x² is transformed to y = (x − 3)² + 3. Where is the new vertex? Type it like (2, −1).

    xy−10−8−6−4−2246810−10−8−6−4−22468100O

    Answer

  16. Question 16

    Which transformation maps y = f(x) to y = f(x + 4)?

    • A. translate up 4
    • B. translate left 4
    • C. reflect in the x-axis
    • D. reflect in the y-axis

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Answer key: Transformations of functions

  1. 1. (−2, −3)

  2. 2. C. reflect in the x-axis

  3. 3. (−6, −2)

  4. 4. C. reflect in the x-axis

  5. 5. (2, −1)

  6. 6. B. translate left 4

  7. 7. (2, 6)

  8. 8. D. reflect in the y-axis

  9. 9. (−5, −3)

  10. 10. B. translate left 4

  11. 11. (3, −1)

  12. 12. C. reflect in the x-axis

  13. 13. (−2, 6)

  14. 14. A. translate up 2

  15. 15. (3, 3)

  16. 16. B. translate left 4