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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.

Minnesota K-12 Academic Standards benchmark: 9.3.7.10; 9.3.7.6 · function notation, and the domain and range of a function

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 Minnesota

In the Minnesota K-12 Academic Standards, 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: Minnesota Department of Education (MDE)

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) = −5x + 1, what is f(−1)?

    answer box

  2. Question 2

    f(x) = 2x − 8. For which x is f(x) = 0?

    • 4
    • 0
    • 5
    • -4

  3. Question 3

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

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

  4. Question 4

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

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

  5. Question 5

    h(t) gives the height of a ball t seconds after it is thrown until it lands at t = 3. Which domain makes sense?

    • Numbers greater than 3
    • All numbers from 0 to 3
    • Whole numbers only
    • All real numbers

  6. Question 6

    If f(x) = −x + 5, what is f(0)?

    answer box

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