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8th grade · Math · Unit 14 of 17

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.

Alabama Course of Study content standard: 8.13; 8.15; 8.17 · functions as one output for each input, comparing functions, and describing graphs in words

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 Alabama

In the Alabama Course of Study, this is unit 14 of 17 in 8th grade Math, after Systems of Equations and before Cones, Cylinders & Spheres.

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: Alabama State Department of Education (ALSDE)

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

    Is this relation a function?

    xy
    35
    15
    2-1
    41
    • No, one input has two different outputs
    • Yes, each input has exactly one output

  2. Question 2

    Which equation is a linear function?

    • y = 1/x
    • y = x²
    • y = x² − 3
    • y = 7 − x

  3. Question 3

    The rule is y = 3x − 3. What is the output when the input is 3?

    answer box

  4. Question 4

    Function A is y = 4x + 9. Function B is shown in the table. Which has the greater rate of change?

    Function B
    xy
    09
    115
    221
    • Function B
    • They are the same
    • Function A

  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
    • Total cost of apples at a fixed price per pound
    • A ball thrown up and coming down

  6. Question 6

    The graph goes up, then comes back down, like a hill. Which situation fits best?

    • The height of a ball thrown into the air
    • The temperature of an oven left on
    • Money in a jar that only gets deposits
    • The distance walked at a steady pace

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