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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

Score/ 16

  1. Question 1

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

    Answer

  2. Question 2

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

    • A. Yes
    • B. No

  3. Question 3

    The function f = {(−2, −4), (8, 5), (2, 7), (−4, 5), (4, 7), (7, −4)}. How many different values are in its range?

    Answer

  4. Question 4

    Which set of ordered pairs is a function?

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

  5. Question 5

    What is the domain of f(x) = √(4 − x) (real numbers only)?

    • A. x ≥ 4
    • B. x ≠ 4
    • C. x > 4
    • D. x ≤ 4

  6. Question 6

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

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

  7. Question 7

    R = {(5, 4), (−5, 8), (−6, −3), (−1, 3)}. What is the range of R?

    • A. {−6, −5, −3, −1, 3, 4, 5, 8}
    • B. {−6, −5, −1, 5}
    • C. {−3, 3, 4, 8}
    • D. {−3, 3, 4}

  8. Question 8

    What is the smallest x in the domain of f(x) = √(5x)?

    Answer

  9. Question 9

    Is this relation a function? {(8, −4), (0, 7), (−5, 9), (1, 0), (−3, 5)}

    • A. Yes
    • B. No

  10. Question 10

    The function f = {(8, 6), (−4, −4), (1, −4), (6, 6), (5, 3), (9, 3)}. How many different values are in its range?

    Answer

  11. Question 11

    Which set of ordered pairs is a function?

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

  12. Question 12

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

    • A. x > 1
    • B. x ≤ 1
    • C. x ≥ 1
    • D. x ≠ 1

  13. Question 13

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

    xy−66−66120(5, −1)(2, −4)(−5, 7)(6, 2)
    • A. Yes
    • B. No

  14. Question 14

    R = {(9, 2), (1, 9), (−1, 7), (3, 4)}. What is the domain of R?

    • A. {−1, 1, 2, 3, 4, 7, 9}
    • B. {−1, 1, 3, 9}
    • C. {2, 4, 7, 9}
    • D. {−1, 1, 3}

  15. Question 15

    What is the smallest x in the domain of f(x) = √(5x + 10)?

    Answer

  16. Question 16

    Is this relation a function? {(0, 2), (−1, −6), (4, 6), (−4, 0), (0, 4)}

    • A. Yes
    • B. No

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Answer key: Domain and range

  1. 1. -1

  2. 2. A. Yes

  3. 3. 3

  4. 4. C. {(2, −4), (−3, 6), (−1, 1), (0, 7)}

  5. 5. D. x ≤ 4

  6. 6. B. No

  7. 7. C. {−3, 3, 4, 8}

  8. 8. 0

  9. 9. A. Yes

  10. 10. 3

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

  12. 12. B. x ≤ 1

  13. 13. A. Yes

  14. 14. B. {−1, 1, 3, 9}

  15. 15. -2

  16. 16. B. No