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Linear, quadratic or exponential?

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

You know three kinds of functions. You learn to see from a table which kind it is: same difference, same factor, or \(x^2\).
📄 Open worksheet (PDF, German)

The video

In the video the tables stand one under the other. Arrows show the difference or the factor.

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

Contents of the video

  1. 0:00 Difference or factor
  2. 0:27 Quadratic
  3. 0:49 The graph
  4. 1:06 Recognising the kind
  5. 1:39 Careful, mistake!
  6. 2:03 Try it yourself

The most important points

Same difference, same factor

Linear \(y = 2x + 1\): \(1, 3, 5, 7, 9\), always \(+2\). Exponential \(y = 2^x\): \(1, 2, 4, 8, 16\), always \(\cdot 2\).

Linear: same difference. Exponential: same factor.
Linear: same difference. Exponential: same factor.

Quadratic \(y = x^2\): \(0, 1, 4, 9, 16\). The differences \(1, 3, 5, 7\) grow. The differences of the differences are always \(2\).

The graph

The line rises evenly, the parabola ever more steeply, the exponential curve fastest in the end. For \(x > 4\) we have \(2^x > x^2\).

Line, parabola and exponential curve compared.
Line, parabola and exponential curve compared.

Recognising the kind: same difference \(\to\) linear, same factor \(\to\) exponential, \(x^2\) \(\to\) quadratic. A plant grows \(2\) cm every day: linear. Bacteria double every hour: exponential.

3, 6, 9, 12: linear, not exponential.
\(3, 6, 9, 12\): linear, not exponential.

Careful: \(3, 6, 9, 12\) is not exponential. The factors \(2\); \(1{,}5\); \(1{,}33\) are different. The difference is always \(3\): linear.

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
Page 1/3
The worksheet – Page 2
Page 2/3
Show the worksheet solutions
The worksheet – Page 3
Page 3/3

Try it yourself

Task

Which kind fits? A: \(5, 8, 11, 14\) and B: \(3, 6, 12, 24\)

Show solution

A: always \(+3\), linear. B: always \(\cdot 2\), exponential.

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: linear, quadratisch oder exponentiell (Wertetabellen: Unterschied, Faktor). 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.