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9th grade · Math · Unit 10 of 17

Function Notation

f(x), domain and range

What your child practices

Evaluating and solving with function notation, and naming the domain and range of a function, including a sensible domain in a real situation.

Maine Learning Results learning standard: HSF.IF.A.1; HSF.IF.A.2; HSF.IF.B.5 · functions as rules, function notation, and the domain of a function in context

How we explain it

Children can open this short lesson before they practice.

  1. f(x) is the output of f when the input is x.
  2. To find f(3), replace every x with 3.
  3. The domain is all the inputs. The range is all the outputs.

Example: f(x) = 2x − 5. What is f(4)? 2 × 4 − 5 = 8 − 5. Answer: 3

Function Notation in Maine

In the Maine Learning Results, this is unit 10 of 17 in 9th grade Math, after Data & Scatter Plots and before Linear Inequalities.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Maine Department of Education

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    If f(x) = −4x + 8, what is f(3)?

    answer box

  2. Question 2

    What is the range of {(−1, 6), (0, −4), (2, 8), (5, −4)}?

    • {−4, 6, 8}
    • {−1, 0, 2, 5}
    • {−4, −1, 0, 2, 5, 6, 8}
    • {−3, 7, 9}

  3. Question 3

    f(x) = −2x − 6. For which x is f(x) = 4?

    • 5
    • 4
    • -5
    • -4

  4. Question 4

    P(w) = 15w gives pay for w whole weeks worked in a 10-week summer job. Which domain makes sense?

    • Any number from 0 to 150
    • Negative whole numbers
    • All real numbers
    • Whole numbers from 0 to 10

  5. Question 5

    What is the range of {(−3, 9), (−1, 3), (1, 6), (2, −2)}?

    • {−1, 4, 7, 10}
    • {−3, −2, −1, 1, 2, 3, 6, 9}
    • {−2, 3, 6, 9}
    • {−3, −1, 1, 2}

  6. Question 6

    C(n) = 8n gives the cost of n movie tickets. Which domain makes sense?

    • All real numbers
    • Whole numbers 0, 1, 2, 3, ...
    • Negative numbers only
    • Numbers between 0 and 1

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