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How does a function represent a relationship?

A function assigns one output to each input in its domain.

MathematicsTopic · Selected readingSome background helpful
Background and goal

Try the short introduction first, or bring equivalent reading experience. Obtain the specified text before beginning the longer reading.

Build a table and rule for a simple subscription cost; explain its domain and one excluded case.

Useful preparation

Start here if the background is new. Equivalent experience is enough.

Your pathway

5 steps · 14 hours
  1. 01

    Locate the reading

    0.25h · week 1
    Reading notes and task
    First fifteen minutesCheck the edition or article version and locate the passages below. Write the question you want the reading to resolve.
    Your outputEdition and passage record
  2. 02

    Study the opening

    4h · week 1
    College Algebra 2e

    OpenStax · book

    Chapter 3, Functions; first sections on notation, domain and range

    Free full text

    Open the reading
    Reading notes and task

    College Algebra 2e. A function assigns one output to each input in its domain.

    Try thisRead Chapter 3, Functions; first sections on notation, domain and range. Reconstruct the central argument using premises and a conclusion.
    Your outputArgument reconstruction
    Check your understanding

    Answer this question in your own words: How does a function represent a relationship?

    Hint

    Name the claim, then explain why a reader might accept it.

    Compare with an example answer

    A function assigns one output to each input in its domain.

    What to look for

    • States a claim that addresses the question
    • Connects the claim to a passage or observation
    • Separates the author’s argument from personal agreement

    Common mistake: Summarising a biography instead of explaining the argument.

    Start this pathway to keep your answers in My learning.

  3. 03

    Read for contrast

    5h · week 2
    College Algebra 2e

    OpenStax · book

    Chapter 3, Functions; first sections on notation, domain and range

    Free full text

    Open the reading
    Reading notes and task

    College Algebra 2e. A function assigns one output to each input in its domain.

    Try thisRead Chapter 3, Functions; first sections on notation, domain and range. Compare two passages that put pressure on your initial interpretation.
    Your outputTwo-passage comparison
  4. 04

    Develop an example

    3h · week 3
    Reading notes and task
    Try thisBuild a table and rule for a simple subscription cost; explain its domain and one excluded case.
    Your outputWorked example
    Check your understanding

    What would make your activity a convincing example?

    Hint

    Build a table and rule for a simple subscription cost; explain its domain and one excluded case.

    Compare with an example answer

    A useful response carries out the task: Build a table and rule for a simple subscription cost; explain its domain and one excluded case. It records the observation or passage used and explains how it bears on the question.

    What to look for

    • Completes the specific task
    • Shows evidence or reasoning rather than only a conclusion
    • Identifies an alternative explanation or reading

    Common mistake: Presenting an opinion without showing the example it rests on.

    Start this pathway to keep your answers in My learning.

  5. 05

    Write a considered response

    1.75h · week 4
    Reading notes and task
    Try thisWrite a response to “How does a function represent a relationship?” that uses both passages and tests its own conclusion. A fitted function does not by itself explain a causal mechanism.
    Your outputReasoned response with references
    Check your understanding

    What is one conclusion this reading does not establish?

    Hint

    Test the boundary: A fitted function does not by itself explain a causal mechanism.

    Compare with an example answer

    A fitted function does not by itself explain a causal mechanism.

    What to look for

    • States a specific limit
    • Explains why the reading does not warrant the stronger conclusion
    • Distinguishes a limitation from dismissing the work

    Common mistake: Treating a useful interpretation as an unrestricted fact.

    Start this pathway to keep your answers in My learning.

All 1 resources

Background, different viewpoints, and further reading.

  • College Algebra 2e

    OpenStaxbookcore

    A function assigns one output to each input in its domain.

    Chapter 3, Functions; first sections on notation, domain and range