Function Notation practice questions

Function Notation questions

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1. 1Function notationFoundation

   If f(x) = 4x + 1 and f(t) = 21, what is the value of t?If f(x) = 4x + 1 and f(t) = 21, what is the value of t?

   • A2020
   • B55
   • C44
   • D66
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   Answer: 55

   f(t) = 21 means 4t + 1 = 21. Then 4t = 20, so t = 5. Function notation is only naming: replace f(t) with the rule and solve the equation you already know how to solve.f(t) = 21 means 4t + 1 = 21. Then 4t = 20, so t = 5. Function notation is only naming: replace f(t) with the rule and solve the equation you already know how to solve.

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2. 2Function notationFoundation

   If f(x) = x/2 + 7, what is the value of f(12)?If f(x) = x/2 + 7, what is the value of f(12)?

   • A1919
   • B1313
   • C9.59.5
   • D2626
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   Answer: 1313

   Substituting gives 122 + 7 = 6 + 7 = 13. Adding before dividing gives 9.5, which is the order-of-operations slip this question tests.Substituting gives 12/2 + 7 = 6 + 7 = 13. Adding before dividing gives 9.5, which is the order-of-operations slip this question tests.

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3. 3Function notationFoundation

   If f(x) = 6 - 2x, what is the value of f(-4)?If f(x) = 6 - 2x, what is the value of f(-4)?

   • A-2-2
   • B22
   • C-14-14
   • D1414
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   Answer: 1414

   Substituting gives 6 - 2(-4) = 6 + 8 = 14. Subtracting a negative adds, which is the whole of this question.Substituting gives 6 - 2(-4) = 6 + 8 = 14. Subtracting a negative adds, which is the whole of this question.

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4. 4Function notationStandard

   If f(x) = 5 - 2x, for what value of x does f(x) = f(1) + 6?If f(x) = 5 - 2x, for what value of x does f(x) = f(1) + 6?

   • A22
   • B-3-3
   • C-2-2
   • D44
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   Answer: -2-2

   First f(1) = 5 - 2 = 3, so the target value is 3 + 6 = 9. Solving 5 - 2x = 9 gives -2x = 4 and x = -2.First f(1) = 5 - 2 = 3, so the target value is 3 + 6 = 9. Solving 5 - 2x = 9 gives -2x = 4 and x = -2.

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5. 5Function notationStandard

   If f(x) = 3x + 2 and g(x) = x - 4, what is f(g(5))?If f(x) = 3x + 2 and g(x) = x - 4, what is f(g(5))?

   • A55
   • B1111
   • C1313
   • D1717
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   Answer: 55

   Work from the inside out: g(5) = 1, then f(1) = 3 + 2 = 5. Applying f first would give a different and incorrect answer.Work from the inside out: g(5) = 1, then f(1) = 3 + 2 = 5. Applying f first would give a different and incorrect answer.

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6. 6Function notationStandard

   If f(x) = x² + 1, which value of x gives f(x) = f(-3)?If f(x) = x^2 + 1, which value of x gives f(x) = f(-3)?

   • A1010
   • B33
   • C99
   • D-9-9
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   Answer: 33

   f(-3) = 10, and f(3) = 10 as well because squaring removes the sign. The value 10 is the output, not the input.f(-3) = 10, and f(3) = 10 as well because squaring removes the sign. The value 10 is the output, not the input.

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7. 7Function notationStandard

   The function g is defined by g(x) = 3x + 2. Enter the value of x for which g(x) = 20.The function g is defined by g(x) = 3x + 2. Enter the value of x for which g(x) = 20.

   Student-produced response: write your own answer rather than choosing one.

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   Answer: 66

   Set 3x + 2 = 20, so 3x = 18 and x = 6. The question asks for the input, not the output, which is the step worth reading twice.Set 3x + 2 = 20, so 3x = 18 and x = 6. The question asks for the input, not the output, which is the step worth reading twice.

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8. 8Function notationStandard

   If f(x) = 4 - x², what is the value of f(-3)?If f(x) = 4 - x^2, what is the value of f(-3)?

   • A1313
   • B-5-5
   • C55
   • D11
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   Answer: -5-5

   Substituting gives 4 - (-3)² = 4 - 9 = -5. The square makes the input positive before it is subtracted; treating the minus as part of the square gives 13.Substituting gives 4 - (-3)^2 = 4 - 9 = -5. The square makes the input positive before it is subtracted; treating the minus as part of the square gives 13.

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9. 9Function notationChallenge

   If f(x) = 2x - 5, what is the value of f(f(3))?If f(x) = 2x - 5, what is the value of f(f(3))?

   • A-1-1
   • B33
   • C-3-3
   • D11
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   Answer: -3-3

   Work from the inside out: f(3) = 6 - 5 = 1, then f(1) = 2 - 5 = -3. The output of the first becomes the input of the second; f(f(3)) is not f(3) doubled.Work from the inside out: f(3) = 6 - 5 = 1, then f(1) = 2 - 5 = -3. The output of the first becomes the input of the second; f(f(3)) is not f(3) doubled.

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10. 10Function notationChallenge

    If f(x) = ax + 3 and f(2) = 11, what is f(5)?If f(x) = ax + 3 and f(2) = 11, what is f(5)?

    • A2626
    • B2020
    • C1919
    • D2323
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    Answer: 2323

    From f(2) = 11: 2a + 3 = 11, so a = 4 and f(x) = 4x + 3. Then f(5) = 20 + 3 = 23.From f(2) = 11: 2a + 3 = 11, so a = 4 and f(x) = 4x + 3. Then f(5) = 20 + 3 = 23.

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11. 11Function notationChallenge

    The function f is defined by f(x) = 5x - 4. If f(a) = 26, what is the value of f(a + 2)?The function f is defined by f(x) = 5x - 4. If f(a) = 26, what is the value of f(a + 2)?

    • A2828
    • B3030
    • C3636
    • D5252
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    Answer: 3636

    From 5a - 4 = 26 comes a = 6, so f(8) = 40 - 4 = 36. Quicker: adding 2 to the input of a linear function with slope 5 adds 10 to the output, and 26 + 10 = 36. Doubling the output gives 52, which the notation does not license.From 5a - 4 = 26 comes a = 6, so f(8) = 40 - 4 = 36. Quicker: adding 2 to the input of a linear function with slope 5 adds 10 to the output, and 26 + 10 = 36. Doubling the output gives 52, which the notation does not license.

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12. 12Function notationChallenge

    If f(x) = 2x - 7 and g(x) = x², what is the value of f(g(3))?If f(x) = 2x - 7 and g(x) = x^2, what is the value of f(g(3))?

    • A1111
    • B11
    • C44
    • D-1-1
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    Answer: 1111

    Work outward from the inside: g(3) = 9, then f(9) = 18 - 7 = 11. Doing it in the other order gives g(f(3)) = g(-1) = 1, which is why the order in the notation matters.Work outward from the inside: g(3) = 9, then f(9) = 18 - 7 = 11. Doing it in the other order gives g(f(3)) = g(-1) = 1, which is why the order in the notation matters.

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