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Curves, Tangents and Asymptotes

Curves, Tangents and Asymptotes

In this feature, we invite you to explore properties of graphs. Can you find functions whose graphs have the given properties? How does a graph change (or stay the same) when you transform it? And what do we really mean by a tangent?

Can You Find ... Cubic Edition 
Age 16 to 18
Challenge Level Yellow star

Can you find cubic functions which satisfy each condition?

Can You Find ... Asymptote Edition 
Age 16 to 18
Challenge Level Yellow star

Given a sketch of a curve with asymptotes, can you find an appropriate function?

A Tangent Is ... 
Age 16 to 18
Challenge Level Yellow star

What do we REALLY mean when we talk about a tangent to a curve?

Transformation ... or Not? 
Age 16 to 18
Challenge Level Yellow star

This graph looks like a transformation of a familiar function...

Related

  • Coordinate Geometry and Graphs
  • Algebra and Functions A2

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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