2.3 Domain and range of a function Quiz: AQA Further Maths, Unit 2

The 20 questions

1. What is the range of f(x) = x^2 when x takes all real values?

   • All real numbers
   • f(x) ≥ 0
   • f(x) > 0
   • f(x) ≤ 0

2. What is the domain of f(x) = √x for real outputs?

   • x ≤ 0
   • x > 0
   • All real numbers
   • x ≥ 0

3. What is the domain of f(x) = 1/(x + 3)?

   • All real x except x = −3
   • All real x except x = 3
   • x > −3
   • All real x except x = 0

4. What set of numbers is represented by the domain x > 2?

   • Reals from 2
   • Reals below 2
   • Reals exceeding 2
   • Integers exceeding 2

5. What is the range of f(x) = 2x − 1 for all real x?

   • f(x) ≥ −1
   • All real numbers
   • f(x) ≤ 1
   • f(x) > 0

6. What is the range of f(x) = x^2 − 3 for all real x?

   • f(x) > −3
   • All real numbers
   • f(x) ≥ −3
   • f(x) ≤ −3

7. For f(x) = x^2 with domain {−2, −1, 0, 1, 2}, what is the range?

   • {−2, −1, 0, 1, 2}
   • {0, 1, 2, 4}
   • {1, 4}
   • {0, 1, 4}

8. For f(x) = 3x − 2 with 1 ≤ x ≤ 4, what is the range?

   • 1 ≤ f(x) ≤ 12
   • 1 ≤ f(x) ≤ 10
   • −1 ≤ f(x) ≤ 10
   • 3 ≤ f(x) ≤ 10

9. For f(x) = 1/x with x > 0, what is the range?

   • f(x) < 0
   • f(x) ≠ 0
   • f(x) ≥ 0
   • f(x) > 0

10. For f(x) = x + 4 with x ≥ −3, what is the range?

    • f(x) ≥ 1
    • f(x) ≥ 4
    • f(x) ≥ −3
    • f(x) ≥ 7

11. For f(x) = √(x − 5), what is the range?

    • f(x) ≥ 0
    • f(x) > 0
    • f(x) ≥ 5
    • All real numbers

12. What is the domain of f(x) = √(4 − x) for real outputs?

    • x ≥ 4
    • x ≤ 4
    • x < 4
    • x ≥ −4

13. For f(x) = x^2 + 2 with 0 ≤ x ≤ 3, what is the range?

    • 0 ≤ f(x) ≤ 11
    • 2 ≤ f(x) ≤ 11
    • 2 ≤ f(x) ≤ 9
    • 2 ≤ f(x) ≤ 5

14. For f(x) = 2/(x − 1) with x > 1, what is the range?

    • f(x) > 2
    • f(x) ≠ 0
    • f(x) > 0
    • f(x) ≥ 2

15. For which values of x is f(x) = x/(x^2 − 9) undefined?

    • x = 3 and x = −3
    • x = 0
    • x = 9 and x = −9
    • x = 3 only

16. For f(x) = x^2 − 6x + 10 over all real x, what is the range?

    • f(x) ≥ 0
    • f(x) ≥ 1
    • f(x) ≥ 10
    • f(x) ≥ −1

17. For f(x) = 3 − x^2 with −1 ≤ x ≤ 2, what is the range?

    • −1 ≤ f(x) ≤ 2
    • −4 ≤ f(x) ≤ 3
    • −1 ≤ f(x) ≤ 3
    • 0 ≤ f(x) ≤ 3

18. What is the domain of f(x) = √(x^2 − 4)?

    • x ≥ 4
    • −2 ≤ x ≤ 2
    • x ≤ −2 or x ≥ 2
    • x ≥ 2

19. What is the range of the function f(x) = 1 / (x² + 1)?

    • 0 ≤ f(x) ≤ 1
    • f(x) ≥ 1
    • 0 < f(x) ≤ 1
    • f(x) > 0

20. What is the domain of f(x) = 1/(x^2 − x − 6)?

    • x ≠ −2 and x ≠ −3
    • x ≠ −2 and x ≠ 3
    • x ≠ 3 only
    • x ≠ 2 and x ≠ −3

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