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8th grade · Math · Unit 15 of 19

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.

New York State Learning Standards learning standard: NY-8.F.1; NY-8.F.2; NY-8.F.3; NY-8.F.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 New York

In the New York State Learning Standards, this is unit 15 of 19 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: 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

    The graph rises steadily, then stays flat, then falls back to zero. Which situation fits best?

    • A bike ride away from home, a rest, then the ride back home
    • A bath filling up and never draining
    • A car that never stops moving
    • A plant that grows faster and faster

  2. Question 2

    The rule is y = −5x + 4. What is the output when the input is −3?

    answer box

  3. Question 3

    Is this relation a function?

    xy
    66
    2-1
    35
    2-3
    • No, one input has two different outputs
    • Yes, each input has exactly one output

  4. Question 4

    Function A is y = 7x + 3. Function B is shown in the table. Which has the greater rate of change?

    Function B
    xy
    00
    15
    210
    • Function A
    • Function B
    • They are the same

  5. Question 5

    Which equation is NOT a linear function?

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

  6. Question 6

    Is this relation a function?

    xy
    35
    15
    5-4
    12
    • No, one input has two different outputs
    • Yes, each input has exactly one output

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