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. A small rule takes the inputs 1, 2 and 3 and returns 5, 8 and 11 in that order. What is its range?

    • 1, 2 and 3
    • 1, 2, 3, 5, 8 and 11
    • 5, 8 and 11
    • 3

  2. What is the smallest input allowed by f(x) = √(x - 5)?

    Answer: ______________

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

    Circle one:   True   False

  4. Which single value of x has to be left out of the domain of f(x) = 1/(x - 7)?

    Answer: ______________

  5. What is the domain of f(x) = 5/(2x - 8)?

    • all real numbers except 8
    • all real numbers except -4
    • x >= 4
    • all real numbers except 4

  6. Omar says the domain of f(x) = √(x - 9) is x > 9, because zero has no square root. Where is the slip?

    • the square root of 0 is 0, so x = 9 is allowed and the domain is x >= 9
    • zero really has no square root, so he is right
    • the domain is all real numbers
    • the domain is x <= 9

  7. The rule f(x) = √(x - 6) can return the output -2.

    Circle one:   True   False

  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. A quadratic has range y >= -7 and its turning point sits at x = 2. Which rule fits?

    • y = (x + 2)² - 7
    • y = (x - 7)² + 2
    • y = -(x - 2)² - 7
    • y = (x - 2)² - 7

  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. 5, 8 and 11 · The range collects what comes out. The numbers going in, 1, 2 and 3, are the domain.
  2. 5 · The inside must be zero or more, so x - 5 >= 0 and x >= 5. The smallest allowed input is 5, where the output is 0.
  3. 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.
  4. 7 · At x = 7 the denominator is 7 - 7 = 0, and dividing by zero has no answer, so 7 is the one input with no output.
  5. all real numbers except 4 · Solve 2x - 8 = 0: 2x = 8, so x = 4. That one input is barred and the rest are fine.
  6. the square root of 0 is 0, so x = 9 is allowed and the domain is x >= 9 · 0 times 0 is 0, so the square root of 0 is 0. The bar is on a negative inside, not on zero.
  7. False · The square root sign returns the root that is not negative, so every output of this rule is 0 or more. Its range is y >= 0.
  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. y = (x - 2)² - 7 · A range of y >= -7 means -7 is the lowest output, so the curve opens upward with its turning point at (2, -7). That is (x - 2)² - 7.
  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.
Worksheet · LightMySky