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Function: unique assignment

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

A function (die Funktion) assigns exactly one \(y\) to each \(x\). Different \(x\) may have the same \(y\).
📄 Open worksheet (PDF, German)

The video

In the video we assign children their birth month and test graphs with vertical lines.

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Introduction
  2. 0:14 The arrow diagram
  3. 0:27 Function
  4. 0:49 The test on the graph
  5. 1:10 Careful, mistake!
  6. 1:31 Try it yourself

The most important points

Unique

Exactly one arrow starts from each \(x\) (eindeutig). Two arrows may arrive at the same \(y\).

Child \to month: unique.
Child \(\to\) month: unique.

Function

A unique assignment is called a function. Month \(\to\) child is not a function: two arrows start from March.

Month \to child: not a function.
Month \(\to\) child: not a function.

On the graph: each vertical line meets the graph at most once. Parabola: function. Circle: not a function.

The test with vertical lines.
The test with vertical lines.

Careful: for \(y = x^2\), \(-2\) and \(2\) have the same \(y = 4\). That is allowed.

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
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The worksheet – Page 2
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The worksheet – Page 3
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Show the worksheet solutions
The worksheet – Page 4
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Try it yourself

Task

Which table belongs to a function? a) \(x\): \(1, 2, 3, 4\), \(y\): \(5, 5, 6, 7\); b) \(x\): \(1, 1, 2, 3\), \(y\): \(2, 4, 6, 8\).

Show solution

a) function: each \(x\) appears only once. b) not a function: \(x = 1\) has two \(y\)-values.

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Funktion als eindeutige Zuordnung (Pfeildiagramm, Tabelle, senkrechte Linie am Graphen). Stelle mir nacheinander fünf kurze Aufgaben. Warte immer auf meine Antwort. Sag mir dann, ob sie richtig ist, und erkläre kurz, warum. Benutze einfache deutsche Sätze.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.