Exponential Graphs

This is a card-sorting activity to generate discussion about exponential graphs. Distribute the graph cards and ask students to sort them using criteria, e.g. (0,1) is on the graph, shape, axes crossed, related graphs.

Can the findings be generalised?

Distribute the equation cards and ask students to match them to the graph cards and discuss. Can an exponential function ever be a straight line? Can an exponential function ever cross the horizontal axis? Why include y〖=x〗^2? Sketch the graph of y〖=5〗^x, identifying key features. Explore the graph of y=a^x for different values of a in Geogebra.

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Overview of task

This is a card-sorting activity to generate discussion about exponential graphs. Distribute the graph cards and ask students to sort them using criteria, e.g. (0,1) is on the graph, shape, axes crossed, related graphs.

Can the findings be generalised?

Distribute the equation cards and ask students to match them to the graph cards and discuss. Can an exponential function ever be a straight line? Can an exponential function ever cross the horizontal axis? Why include y〖=x〗^2? Sketch the graph of y〖=5〗^x, identifying key features. Explore the graph of y=a^x for different values of a in Geogebra.

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Strand

Algebra and Graphs

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Prior knowledge

Understand powers and indices, e.g. 2^3=2×2×2

Recognise y=2x+3 as a graph and generate coordinates such as (5,13)

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Relevance to Core Maths qualifications

  • AQA
  • C&G
  • Eduqas
  • Pearson / Edexcel
  • OCR

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Suggested approaches

Small group work and discussion.

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Resources/documentation

Cards for card sort task (PowerPoint); Geogebra resource

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Relevant digital technologies

Graphing software, calculator, Geogebra

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Possible extensions

Discuss the effect of transforming functions:

Given f(x)=2^x what would the graph of y=f(x+2) look like?

Discuss the graph of y=(-2)^x

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Acknowledgement

Developed by Karl Aughton at Outwood Academy, Ripon.