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
Can you find cubic functions which satisfy each condition?

Can You Find ... Asymptote Edition 

Age 16 to 18
Challenge Level
Given a sketch of a curve with asymptotes, can you find an appropriate function?

A Tangent Is ... 

Age 16 to 18
Challenge Level
What do we REALLY mean when we talk about a tangent to a curve?

Transformation ... or Not? 

Age 16 to 18
Challenge Level
This graph looks like a transformation of a familiar function...