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What is a function?: 8th grade math

Function as exactly one output per input. A free 8th grade lesson plan, a question set with answers and a printable sheet with its key. Copy it and make it yours.

Lesson plan

Goal

  • Students can do this: function as exactly one output per input.

Teach (10 min)

  • 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.
  • Work one example on the board while students say each step aloud, then do one together.

Practise (15 min)

  • Students work the printable sheet in pairs, then alone.
  • Or practise it as a game with no sign-up: https://peabody.kids/math/funcs.isFunc?lesson=8-funcs-isfunc-1&at=8

Exit ticket (5 min)

  • Three questions on a slip:
  • 1. Here are input-output pairs (input, output): (8, 3), (4, 7), (5, 6), (5, 9). Is the output a function of the input?
  • 2. Here are input-output pairs (input, output): (2, 2), (3, 8), (2, 1). Is the output a function of the input?
  • 3. Here are input-output pairs (input, output): (8, 6), (1, 9), (6, 5). Is the output a function of the input?

Question set

10 questions that read in words, easiest first. Questions that need a picture are on the printable sheet below.

  1. Here are input-output pairs (input, output): (8, 3), (4, 7), (5, 6), (5, 9). Is the output a function of the input?
  2. Here are input-output pairs (input, output): (2, 2), (3, 8), (2, 1). Is the output a function of the input?
  3. Here are input-output pairs (input, output): (8, 6), (1, 9), (6, 5). Is the output a function of the input?
  4. Look at the table. Input: 2, 8, 2, 1 Output: 9, 4, 6, 3 Is the output a function of the input?
  5. Look at the table. Input: 6, 9, 9 Output: 6, 5, 7 Is the output a function of the input?
  6. Here are input-output pairs (input, output): (1, 7), (3, 1), (3, 4). Is the output a function of the input?
  7. Here are input-output pairs (input, output): (1, 8), (1, 5), (4, 9). Is the output a function of the input?
  8. Here are input-output pairs (input, output): (7, 5), (2, 4), (8, 8). Is the output a function of the input?
  9. Look at the table. Input: 3, 7, 4, 1 Output: 1, 4, 2, 7 Is the output a function of the input?
  10. Look at the table. Input: 3, 5, 2 Output: 8, 1, 5 Is the output a function of the input?
Answers
  1. No, one input has two different outputs
  2. No, one input has two different outputs
  3. Yes, each input has exactly one output
  4. No, one input has two different outputs
  5. No, one input has two different outputs
  6. No, one input has two different outputs
  7. No, one input has two different outputs
  8. Yes, each input has exactly one output
  9. Yes, each input has exactly one output
  10. Yes, each input has exactly one output

Printable sheet

Name: ____________________   Date: ____________

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?
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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