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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.

Arizona Academic Standards learning standard: 8.F.A.1; 8.F.A.2; 8.F.A.3; 8.F.B.5 · functions as one output for each input, comparing functions, linear 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 Arizona

In the Arizona Academic Standards, 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: Arizona 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

    Is this relation a function?

    xy
    24
    6-2
    13
    63
    • No, one input has two different outputs
    • Yes, each input has exactly one output

  2. Question 2

    The graph starts high and drops quickly, then more and more slowly. Which situation fits best?

    • A runner speeding up
    • A cup of hot cocoa cooling down on a table
    • A savings account that keeps growing
    • Water filling a tank at a steady rate

  3. Question 3

    Function A is y = 7x + 7. Function B is shown in the table. Which has the greater rate of change?

    Function B
    xy
    08
    111
    214
    • Function B
    • They are the same
    • Function A

  4. Question 4

    Which equation is NOT a linear function?

    • y = −2x + 5
    • y = 0.5x + 4
    • y = 7 − x
    • y = 1/x

  5. Question 5

    The rule is y = 3x + 7. What is the output when the input is −2?

    answer box

  6. Question 6

    The graph starts high and drops quickly, then more and more slowly. Which situation fits best?

    • A cup of hot cocoa cooling down on a table
    • A runner speeding up
    • Water filling a tank at a steady rate
    • A savings account that keeps growing

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