2.2 Definition of a function Quiz: AQA Further Maths, Unit 2

The 20 questions

1. How many outputs can a valid function give for a single input?

   • Infinitely many
   • Exactly one
   • At least two
   • Zero or more

2. For f(x) = 2x + 5, what is f(3)?

   • 17
   • 11
   • 8
   • 13

3. For g(x) = x^2 − 1, what is g(−2)?

   • 3
   • 5
   • −3
   • −5

4. Which set of ordered pairs does NOT define a function?

   • {(1, 2), (2, 3), (1, 4)}
   • {(1, 2), (2, 3), (3, 4)}
   • {(0, 0), (1, 1), (2, 4)}
   • {(1, 2), (2, 2), (3, 2)}

5. For f(x) = x − 9, what is f(10)?

   • 19
   • −1
   • 1
   • 9

6. For h(x) = 3x − 4, what value of x gives h(x) = 8?

   • 4/3
   • 4
   • 2
   • 12

7. In the standard function notation f(x), what does f(x) represent?

   • The output value
   • The input value
   • The gradient
   • The domain

8. For p(x) = 1/x, what is p(4)?

   • 0.25
   • 4
   • −0.25
   • 0.4

9. Let f(x) = 2x for x < 0 and f(x) = x + 1 for x ≥ 0. What is f(−3) + f(2)?

   • 9
   • −3
   • −9
   • 3

10. For f(x) = x^2 + 3x, which expression is f(a + 1)?

    • a^2 + 5a + 4
    • a^2 + 5a + 1
    • a^2 + 2a + 4
    • a^2 + 3a + 4

11. For f(x) = 3x − 12, what value of k makes f(k) = 0?

    • 12
    • 3
    • 4
    • −4

12. For f(x) = 4x − 1, what is f(f(1))?

    • 15
    • 7
    • 11
    • 3

13. For h(x) = 1/(x − 2), which input value is not allowed?

    • 1
    • 0
    • −2
    • 2

14. A mapping sends 1 to a, 2 to b, and 3 to a. What type of mapping is this?

    • One-to-one function
    • One-to-many mapping
    • Many-to-one function
    • Not a function

15. For f(x) = (x + 1)/(x − 1), what is f(3)?

    • 2
    • 0.5
    • 1
    • 4

16. For f(x) = x^2 + 4x, find the value of x for which f(x) = f(−x).

    • −4
    • 4
    • 2
    • 0

17. For f(x) = 2x + k, f(3) = 11. What is k?

    • 8
    • −5
    • 5
    • 4

18. For f(x) = x^2 − 2x, which values of x satisfy f(x) = 3?

    • −3 or 1
    • 3 or 1
    • 3 or −1
    • −3 or −1

19. f(x) = x^2 for x < 2 and f(x) = 2x for x ≥ 2. What is f(1) + f(2) + f(3)?

    • 7
    • 12
    • 9
    • 11

20. For f(x) = 3x + 2, which value of a satisfies f(a) = a?

    • −2
    • −1
    • 2
    • 1

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