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 g(x) = x squared + 2. What is g(-3)?

    Answer: ______________

  2. The rule is f(x) = 5x + 2. What is f(0)?

    • 0
    • 5
    • 2
    • 7

  3. Under a single rule f, how many outputs can one input give?

    • Exactly one
    • Up to two
    • As many as the rule likes
    • None

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

    Answer: ______________

  5. The rule is f(x) = 5x + 2. Which input gives the output 12?

    Answer: ______________

  6. The rule is f(x) = 2x squared - 1. What is f(-3)?

    • 5
    • -7
    • 11
    • 17

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

    • 5x + 2
    • 5x + 7
    • 5x + 1
    • 5x + 12

  8. 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, because 2(3) squared is 36 - 3
    • The 2 should be squared as well, giving 4 times 9 - 3
    • Sam should subtract 3 before squaring
    • The square binds to the 3 only: 3 squared is 9, so f(3) is 2 times 9 - 3 = 15

  9. The rule g(x) = ax + b satisfies g(1) = 3 and g(2) = 7. What is g(4)?

    Answer: ______________

  10. The rule is f(x) = (2x - 1)(x - 3). What is the sum of the two inputs that give the output 0?

    Answer: ______________

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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. 11 · Square the input first: (-3) squared is 9. Then add 2 to get 11.
  2. 2 · Feed 0 into the rule: 5 times 0 is 0, plus 2 is 2. The output at zero is always the constant term.
  3. Exactly one · A rule is a machine: one input goes in, exactly one output comes out. Two inputs may share an output, but one input never has two.
  4. 12 · Feed 2 into the rule: 5 times 2 is 10, plus 2 is 12.
  5. 2 · Set the rule equal to 12: 5x + 2 = 12, so 5x = 10 and x is 2.
  6. 17 · Square the input first: (-3) squared is 9. Then 2 times 9 is 18, minus 1 is 17.
  7. 5x + 7 · The x in the brackets is a placeholder, so feed in x + 1: 5(x + 1) + 2 = 5x + 5 + 2 = 5x + 7.
  8. The square binds to the 3 only: 3 squared is 9, so f(3) is 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.
  9. 15 · From g(1) = 3, a + b = 3, and from g(2) = 7, 2a + b = 7. Subtracting gives a = 4, so b is -1, and g(4) is 16 - 1 = 15.
  10. 3.5 · Set the rule to zero: 2x - 1 = 0 gives x = 0.5, and x - 3 = 0 gives x = 3. The sum is 3.5.
Worksheet · LightMySky