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9th grade · Math · Unit 10 of 22

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.

New York State Learning Standards learning standard: AI-F.IF.1; AI-F.IF.2; AI-F.IF.5 · functions, 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 New York

In the New York State Learning Standards, this is unit 10 of 22 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: New York State Education Department (NYSED)

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

    f(x) = −4x + 9. For which x is f(x) = 1?

    • 1
    • 3
    • 2
    • -2

  2. Question 2

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

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

  3. Question 3

    If f(x) = −4x + 9, what is f(1)?

    answer box

  4. Question 4

    What is the range of {(−3, −3), (0, 9), (2, 8), (4, 3)}?

    • {−3, 0, 2, 3, 4, 8, 9}
    • {−2, 4, 9, 10}
    • {−3, 3, 8, 9}
    • {−3, 0, 2, 4}

  5. Question 5

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

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

  6. Question 6

    If f(x) = x − 4, what is f(3)?

    answer box

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