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8th grade · Math · Unit 10 of 11

Functions

One input, one output

What your child practices

Deciding whether a relation is a function, comparing two functions shown in different ways, spotting linear functions, and matching a graph to a story.

Minnesota K-12 Academic Standards benchmark: 8.3.7.3; 8.3.7.2 · functions as one output for each input, and linear and non-linear patterns

How we explain it

Children can open this short lesson before they practice.

  1. A function gives each input exactly one output.
  2. A repeated x with two different y-values is not a function.
  3. A linear function has a constant rate of change: y = mx + b.

Example: Is {(1, 4), (2, 5), (1, 6)} a function? The input 1 has two outputs, 4 and 6. Answer: No

Functions in Minnesota

In the Minnesota K-12 Academic Standards, this is unit 10 of 11 in 8th grade Math, after Systems of Equations and before Slope & Rate of Change.

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

    Function A is y = 6x + 3. Function B is shown in the table. Which has the greater rate of change?

    Function B
    xy
    05
    110
    215
    • Function B
    • They are the same
    • Function A

  2. Question 2

    The rule is y = −5x − 9. What is the output when the input is 6?

    answer box

  3. Question 3

    Which equation is NOT a linear function?

    • y = 3x − 1
    • y = x²
    • y = 7 − x
    • y = 0.5x + 4

  4. Question 4

    Is this relation a function?

    xy
    27
    50
    47
    31
    • Yes, each input has exactly one output
    • No, one input has two different outputs

  5. Question 5

    The graph is a straight line going up from the origin. Which situation fits best?

    • The height of a swing over time
    • A phone battery that is charging and then unplugged
    • A ball thrown up and coming down
    • Total cost of apples at a fixed price per pound

  6. Question 6

    Which equation is NOT a linear function?

    • y = −2x + 5
    • y = 1/x
    • y = x
    • y = 3x − 1

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