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🧩 8th grade math · Patterns & Algebra

What is a function?

It is a function when each input has exactly one output. (1, 4), (2, 6), (3, 4): every input is used once, so it is a function. (1, 4), (1, 7) is not: the input 1 has two outputs.

Worked example

Here are input-output pairs (input, output): (4, 6), (6, 5), (6, 8). Is the output a function of the input?
Answer: No, one input has two different outputs
The input 6 is paired with both 5 and 8. A function gives exactly one output for each input, so this is not a function. The answer is No, one input has two different outputs.

For grown-ups: Function as exactly one output per input. Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.

  • CCSS 8.F.A.1
What this practises, for teachers

Practices function as exactly one output per input (8.F.A.1). A printable sheet with its answer key, worked answers on the page, no accounts.

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For your class

🖨️ Printable sheet and key

Try three

  1. Here are input-output pairs (input, output): (8, 3), (4, 7), (5, 6), (5, 9). Is the output a function of the input?
    Show the answer and how
    Answer: No, one input has two different outputs
    The input 5 is paired with both 6 and 9. A function gives exactly one output for each input, so this is not a function. The answer is No, one input has two different outputs.
  2. Here are input-output pairs (input, output): (2, 2), (3, 8), (2, 1). Is the output a function of the input?
    Show the answer and how
    Answer: No, one input has two different outputs
    The input 2 is paired with both 2 and 1. A function gives exactly one output for each input, so this is not a function. The answer is No, one input has two different outputs.
  3. Look at the table.
    Input: 3, −4, 1, 0
    Output: 4, 4, 4, 4
    Is the output a function of the input?
    Show the answer and how
    Answer: Yes, each input has exactly one output
    Check every input: each one appears with only one output, so it is a function. (Different inputs may share an output.) The answer is Yes, each input has exactly one output.

Before and after

Learn first: Function machines (4th)

Comes next: Compare functions (8th)

Name: ____________________Date: ____________Score: ____ / 12

What is a function? (8th grade)

  1. Look at the table.
    Input: 6, 1, 8, 2
    Output: 6, 1, 7, 6
    Is the output a function of the input?
  2. Here are input-output pairs (input, output): (2, 6), (3, 7), (3, 9). Is the output a function of the input?
  3. Look at the table.
    Input: 3, 8, 5, 3
    Output: 7, 2, 2, 5
    Is the output a function of the input?
  4. Here are input-output pairs (input, output): (5, 4), (8, 3), (7, 4). Is the output a function of the input?
  5. Here are input-output pairs (input, output): (8, 8), (7, 6), (7, 7), (5, 1). Is the output a function of the input?
  6. Look at the table.
    Input: 2, 8, 3, 6
    Output: 2, 4, 6, 7
    Is the output a function of the input?
  7. Look at the table.
    Input: 3, 2, 9, 8
    Output: 9, 5, 9, 6
    Is the output a function of the input?
  8. Each dot on the graph is an (input, output) pair. Is the output a function of the input?
    −6−5−4−3−2−1123456−6−5−4−3−2−1123456
  9. Look at the table.
    Input: 1, 0, 2, 3, 4
    Output: −1, 5, 0, −4, 3
    Is the output a function of the input?
  10. Each dot on the graph is an (input, output) pair. Is the output a function of the input?
    −6−5−4−3−2−1123456−6−5−4−3−2−1123456
  11. Each dot on the graph is an (input, output) pair. Is the output a function of the input?
    −6−5−4−3−2−1123456−6−5−4−3−2−1123456
  12. Look at the table.
    Input: −3, 0, −4, −4, 4, 3
    Output: 5, 1, 3, 0, −4, −5
    Is the output a function of the input?

Answer key

  1. Yes, each input has exactly one output
  2. No, one input has two different outputs
  3. No, one input has two different outputs
  4. Yes, each input has exactly one output
  5. No, one input has two different outputs
  6. Yes, each input has exactly one output
  7. Yes, each input has exactly one output
  8. No, one input has two different outputs
  9. Yes, each input has exactly one output
  10. No, one input has two different outputs
  11. Yes, each input has exactly one output
  12. No, one input has two different outputs

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