Function Evaluation practice questions

Function Evaluation questions

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1. 1Function evaluationFoundation

   If h(x) = (x + 2)² - 5, what is h(1)?If h(x) = (x + 2)^2 - 5, what is h(1)?

   • A11
   • B44
   • C-4-4
   • D99
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   Answer: 44

   Substitute, then work outwards from the bracket: h(1) = (1 + 2)² - 5 = 3² - 5 = 9 - 5 = 4. Squaring the sum, not the terms, is the order that matters.Substitute, then work outwards from the bracket: h(1) = (1 + 2)^2 - 5 = 3^2 - 5 = 9 - 5 = 4. Squaring the sum, not the terms, is the order that matters.

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2. 2Function evaluationFoundation

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

   • A-4-4
   • B1212
   • C44
   • D-12-12
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   Answer: 1212

   Substitute, keeping the signs: (-2)² - 4(-2) = 4 + 8 = 12. Subtracting a negative adds, which is where this one usually goes wrong — 4 - 8 = -4 is the waiting answer.Substitute, keeping the signs: (-2)^2 - 4(-2) = 4 + 8 = 12. Subtracting a negative adds, which is where this one usually goes wrong — 4 - 8 = -4 is the waiting answer.

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3. 3Function evaluationFoundation

   If p(x) = x³ - 2x, enter the value of p(3).If p(x) = x^3 - 2x, enter the value of p(3).

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

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   Answer: 2121

   Substitute x = 3 and follow the order of operations: 3³ - 2(3) = 27 - 6 = 21. The cube is evaluated before the multiplication, not after.Substitute x = 3 and follow the order of operations: 3^3 - 2(3) = 27 - 6 = 21. The cube is evaluated before the multiplication, not after.

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4. 4Function evaluationFoundation

   If h(x) = 2x² - x, enter the value of h(-3).If h(x) = 2x^2 - x, enter the value of h(-3).

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

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   Answer: 2121

   Substitute x = -3: 2(9) - (-3) = 18 + 3 = 21. The minus sign in front of x makes the second term positive here.Substitute x = -3: 2(9) - (-3) = 18 + 3 = 21. The minus sign in front of x makes the second term positive here.

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5. 5Function evaluationStandard

   The function h is defined by h(x) = x² - 4x. Enter the value of h(-2).The function h is defined by h(x) = x^2 - 4x. Enter the value of h(-2).

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

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   Answer: 1212

   Substituting gives (-2)² - 4(-2) = 4 + 8 = 12. Both signs matter: squaring a negative makes it positive, and subtracting a negative adds.Substituting gives (-2)^2 - 4(-2) = 4 + 8 = 12. Both signs matter: squaring a negative makes it positive, and subtracting a negative adds.

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6. 6Function evaluationStandard

   The function f is defined by f(x) = 2x² - 3x. Enter the value of f(-3).The function f is defined by f(x) = 2x^2 - 3x. Enter the value of f(-3).

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

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   Answer: 2727

   Substituting gives 2(-3)² - 3(-3) = 2(9) + 9 = 18 + 9 = 27. Both signs matter: the square makes the first term positive and subtracting a negative adds.Substituting gives 2(-3)^2 - 3(-3) = 2(9) + 9 = 18 + 9 = 27. Both signs matter: the square makes the first term positive and subtracting a negative adds.

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7. 7Function evaluationStandard

   The function g is defined by g(x) = x² + 2x. Enter the value of g(-4).The function g is defined by g(x) = x^2 + 2x. Enter the value of g(-4).

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

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   Answer: 88

   Substituting gives (-4)² + 2(-4) = 16 - 8 = 8. The square is positive and the second term is negative, so the two partly cancel.Substituting gives (-4)^2 + 2(-4) = 16 - 8 = 8. The square is positive and the second term is negative, so the two partly cancel.

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8. 8Function evaluationStandard

   The function h is defined by h(x) = x² - 5x. Enter the value of h(-3).The function h is defined by h(x) = x^2 - 5x. Enter the value of h(-3).

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

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   Answer: 2424

   Substituting gives (-3)² - 5(-3) = 9 + 15 = 24. The square is positive and subtracting a negative adds, so both terms are positive.Substituting gives (-3)^2 - 5(-3) = 9 + 15 = 24. The square is positive and subtracting a negative adds, so both terms are positive.

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9. 9Function evaluationChallenge

   If f(x) = x² - 4 and f(a) = 21, what are the possible values of a?If f(x) = x^2 - 4 and f(a) = 21, what are the possible values of a?

   • A17 and -1717 and -17
   • B25 and -2525 and -25
   • C5 only5 only
   • D5 and -55 and -5
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   Answer: 5 and -55 and -5

   Solving x² - 4 = 21 gives x² = 25, so a is 5 or -5. Reporting only the positive root answers half the question.Solving x^2 - 4 = 21 gives x^2 = 25, so a is 5 or -5. Reporting only the positive root answers half the question.

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10. 10Function evaluationChallenge

    If f(x) = 2x + 1 and g(x) = x², what is g(f(2))?If f(x) = 2x + 1 and g(x) = x^2, what is g(f(2))?

    • A99
    • B1717
    • C2525
    • D55
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    Answer: 2525

    Work from the inside: f(2) = 5, then g(5) = 25. Applying g first would give f(4) = 9, which is the trap.Work from the inside: f(2) = 5, then g(5) = 25. Applying g first would give f(4) = 9, which is the trap.

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11. 11Function evaluationChallenge

    If f(x) = x² + 1, which expression is equal to f(x + 1) - f(x)?If f(x) = x^2 + 1, which expression is equal to f(x + 1) - f(x)?

    • A11
    • Bx² + 2xx^2 + 2x
    • C2x2x
    • D2x + 12x + 1
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    Answer: 2x + 12x + 1

    f(x + 1) = (x + 1)² + 1 = x² + 2x + 2. Subtracting f(x) = x² + 1 leaves 2x + 1. Treating f(x + 1) as f(x) + 1 gives 1, which is the error the question exists to catch.f(x + 1) = (x + 1)^2 + 1 = x^2 + 2x + 2. Subtracting f(x) = x^2 + 1 leaves 2x + 1. Treating f(x + 1) as f(x) + 1 gives 1, which is the error the question exists to catch.

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