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Domain and range

Grades 8 to 11 (Years 10 to 13 in England) · 16 questions · Common Core: HSF.IF.A.1, HSF.IF.B.5 · England: GCSE Higher Algebra, A-level Pure Mathematics

Name

Date

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  1. Question 1

    R = {(8, 2), (−3, −6), (5, −5), (−6, 8)}. What is the range of R?

    • A. {−6, −5, 2, 8}
    • B. {−6, −5, −3, 2, 5, 8}
    • C. {−6, −5, 2}
    • D. {−6, −3, 5, 8}

  2. Question 2

    Which set of ordered pairs is a function?

    • A. {(−4, −1), (6, 6), (1, 4), (4, 3)}
    • B. {(−3, 2), (−2, −2), (−1, −4), (−1, −5)}
    • C. {(−3, 2), (5, −3), (0, −4), (5, −1)}
    • D. {(−2, −3), (−1, 5), (−3, 2), (−2, −1)}

  3. Question 3

    The graph shows a set of points. Do they represent a function of x?

    xy−66−66120(5, 2)(−3, 1)(0, 7)(−4, 7)
    • A. Yes
    • B. No

  4. Question 4

    Is this relation a function? {(3, 8), (6, 7), (−5, 2), (−4, −5), (1, 6)}

    • A. Yes
    • B. No

  5. Question 5

    What is the domain of f(x) = 1/√(x − 5) (real numbers only)?

    • A. x > 5
    • B. x ≠ 5
    • C. x ≤ 5
    • D. x ≥ 5

  6. Question 6

    The function f = {(1, −2), (−4, 8), (6, 6), (−2, 8), (2, 6), (5, −2)}. How many different values are in its range?

    Answer

  7. Question 7

    What is the smallest x in the domain of f(x) = √(3x − 6)?

    Answer

  8. Question 8

    R = {(−5, 4), (−4, −5), (0, −6), (5, 7)}. What is the domain of R?

    • A. {−6, −5, −4, 0, 4, 5, 7}
    • B. {−5, −4, 0}
    • C. {−6, −5, 4, 7}
    • D. {−5, −4, 0, 5}

  9. Question 9

    Which set of ordered pairs is a function?

    • A. {(−3, −2), (3, 7), (6, 3), (3, 6)}
    • B. {(0, −3), (2, −2), (3, 5), (3, 6)}
    • C. {(−3, −3), (1, 6), (−2, −4), (−2, −7)}
    • D. {(6, 7), (−1, 3), (−2, 5), (−4, 6)}

  10. Question 10

    The graph shows a set of points. Do they represent a function of x?

    xy−66−66120(2, −3)(3, 1)(5, −3)(1, 1)
    • A. Yes
    • B. No

  11. Question 11

    Is this relation a function? {(−6, 5), (6, 2), (2, 3), (8, 3), (0, 4)}

    • A. Yes
    • B. No

  12. Question 12

    What is the domain of f(x) = √(x − 3) (real numbers only)?

    • A. x > 3
    • B. x ≠ 3
    • C. x ≤ 3
    • D. x ≥ 3

  13. Question 13

    The function f = {(0, 8), (7, 7), (4, −1), (3, −1), (−5, 8), (6, 7)}. How many different values are in its range?

    Answer

  14. Question 14

    What is the smallest x in the domain of f(x) = √(4x + 8)?

    Answer

  15. Question 15

    R = {(−1, 1), (−3, 5), (−5, −4), (7, 4)}. What is the domain of R?

    • A. {−5, −3, −1}
    • B. {−5, −4, −3, −1, 1, 4, 5, 7}
    • C. {−5, −3, −1, 7}
    • D. {−4, 1, 4, 5}

  16. Question 16

    Which set of ordered pairs is a function?

    • A. {(−2, 2), (3, 0), (5, −1), (3, 2)}
    • B. {(0, 0), (−1, 5), (2, 7), (2, 9)}
    • C. {(−4, 0), (5, 7), (−1, −3), (6, −4)}
    • D. {(5, −4), (−4, −1), (−1, 5), (−1, 7)}

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Answer key: Domain and range

  1. 1. A. {−6, −5, 2, 8}

  2. 2. A. {(−4, −1), (6, 6), (1, 4), (4, 3)}

  3. 3. A. Yes

  4. 4. A. Yes

  5. 5. A. x > 5

  6. 6. 3

  7. 7. 2

  8. 8. D. {−5, −4, 0, 5}

  9. 9. D. {(6, 7), (−1, 3), (−2, 5), (−4, 6)}

  10. 10. A. Yes

  11. 11. A. Yes

  12. 12. D. x ≥ 3

  13. 13. 3

  14. 14. -2

  15. 15. C. {−5, −3, −1, 7}

  16. 16. C. {(−4, 0), (5, 7), (−1, −3), (6, −4)}