Function notation and evaluating functions · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Function notation and evaluating functions

Mathematics · Algebra · ages 15-16
Name ______________________   Date ____________

  1. The rule is f(x) = 5x + 2. What is f(-1)?

    Answer: ______________

  2. For a function f, how many outputs does each allowed input have?

    • Exactly one
    • Up to two
    • Any number of outputs
    • None

  3. Use f(t) = t² - 4t to calculate the output for input -2.

    Answer: ______________

  4. The rule is f(x) = 2x + 3. What is f(3)?

    • 9
    • 6
    • 12
    • 15

  5. Sam works out f(3) for the rule f(x) = 2x squared - 3. He squares the 2 and the 3 together and gets 33. Where is the slip?

    • 33 is correct: (2 times 3)² - 3 = 33
    • Square 2 too: 4 times 9 - 3
    • Subtract 3 before squaring
    • Square only 3: 2 times 9 - 3 = 15

  6. For the rule g(x) = x squared - 11, the inputs 2 and -2 give the same output.

    Circle one:   True   False

  7. The rule is g(x) = x squared + 3x - 10. Which inputs give the output 0?

    • 5 and 2
    • -5 and -2
    • 5 and -2
    • -5 and 2

  8. Which inputs give zero under f(t) = t² - 4t?

    • t = 0 or t = 4
    • t = 0 or t = -4
    • t = 4 only
    • t = -4 or t = 4

  9. The rule f(x) = x squared - 6x + 9 gives the output 0 for exactly one input.

    Circle one:   True   False

  10. The rule f(x) = x² + 4x + 5 gives output 0 for at least one real input.

    Circle one:   True   False

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Function notation and evaluating functions W1-mt_YWKWzHK_6Z-s1

  1. -3 · Feed -1 into the rule: 5 times -1 is -5, plus 2 is -3.
  2. Exactly one · A function assigns exactly one output to each allowed input. Different inputs may still share an output.
  3. 12 · The square is 4 and the product 4(-2) is -8. Subtracting gives 4 - (-8) = 12.
  4. 9 · Feed 3 into the rule: 2 times 3 is 6, plus 3 is 9.
  5. Square only 3: 2 times 9 - 3 = 15 · In 2x squared, the square applies to the x only. At x = 3: 3 squared is 9, 2 times 9 is 18, minus 3 is 15. Sam squared the product 2 times 3 instead, getting 36 - 3 = 33.
  6. True · Both 2 squared and (-2) squared are 4, so g(2) and g(-2) are both 4 - 11 = -7. Two inputs may share an output.
  7. -5 and 2 · Set the rule to zero: x squared + 3x - 10 = 0 factors as (x + 5)(x - 2), so the inputs are -5 and 2.
  8. t = 0 or t = 4 · Set t² - 4t = 0 and factor out t. Setting each factor equal to zero gives 0 or 4.
  9. True · Set the rule to zero: x squared - 6x + 9 = 0 is (x - 3) squared, so the only input that gives 0 is 3.
  10. False · The rule equals (x + 2)² + 1. A real square is nonnegative, so the output is at least 1 and cannot be zero.
Worksheet · LightMySky