Domain and Range of a Function · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Domain and Range of a Function

Mathematics · Algebra · ages 16-17
Name ______________________   Date ____________

  1. What is the domain of g(x) = 1/(x + 2)?

    • all real numbers except 2
    • all real numbers except -2
    • x >= -2
    • all real numbers

  2. Every real number is an allowed input for h(x) = x² - 4x + 9.

    Circle one:   True   False

  3. Mia says 3 is left out of the domain because 3 - 3 = 0 and division by zero has no value. Is Mia right?

    Circle one:   True   False

  4. The crew calls a rule's allowed inputs its domain. What does the range name?

    • the values the rule can hand back
    • the inputs the rule will accept
    • the input that makes the rule zero
    • how steep the rule is

  5. y = x^2 + 6x + 5 has its turning point at x = -3. What is the smallest value y takes?

    Answer: ______________

  6. h(x) = x² - 8x + 21. What is its range?

    • h(x) >= 21
    • h(x) >= 4
    • h(x) >= 5
    • h(x) >= -5

  7. What is the range of y = (x - 5)² + 4?

    • y >= 4
    • y >= 5
    • y >= 0
    • y >= 9

  8. A path edging x metres long is cut from a 30 m roll. Which domain makes sense for x?

    • all real numbers
    • 0 < x <= 30
    • x <= 30
    • x >= 30

  9. For f(x) = √(10 - 2x), what is the largest allowed input?

    Answer: ______________

  10. What is the domain of f(x) = (√(x - 1))/(x - 4)?

    • x >= 1
    • x >= 1 and x is not 4
    • all real numbers except 4
    • x > 4
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Answer key

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

Domain and Range of a Function W1-mt_b_4zoHz8Jc-s1

  1. all real numbers except -2 · Solving x + 2 = 0 gives x = -2, so -2 is the barred input and every other real number works.
  2. True · There is no denominator and no square root, so nothing can break. A quadratic squares, multiplies and adds, and every real number survives all three.
  3. True · Mia is right: 3 - 3 = 0, and division by zero has no value, so 3 cannot be an input.
  4. the values the rule can hand back · One set goes in and one set comes out. The inputs are the domain, and what comes out is the range.
  5. -4 · At x = -3, y = 9 - 18 + 5 = -4, and the upward curve never goes lower.
  6. h(x) >= 5 · Completing the square gives (x - 4)² + 5, because (x - 4)² is x² - 8x + 16 and 16 + 5 = 21. The lowest output is 5.
  7. y >= 4 · The square is never negative, so its smallest value is 0 at x = 5, and then y = 4. Every output above 4 is reached too.
  8. 0 < x <= 30 · A cut length has to be more than 0, and it cannot beat the 30 m the roll holds. The whole roll is allowed, so 30 stays in.
  9. 5 · The inside must be zero or more: 10 - 2x >= 0 gives 10 >= 2x, so x <= 5. Here the domain runs the other way and stops at 5.
  10. x >= 1 and x is not 4 · Two restrictions apply at once. The root needs x - 1 >= 0, so x >= 1, and the denominator bars x = 4. Both must hold.
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