Curves, Tangents and Asymptotes

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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 link

Can You Find ... Cubic Edition 

Stage: 5 Challenge Level: Challenge Level:1

Can you find cubic functions which satisfy each condition?

Can You Find ... Asymptote Edition link

Can You Find ... Asymptote Edition 

Stage: 5 Challenge Level: Challenge Level:1

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

A Tangent Is ... link

A Tangent Is ... 

Stage: 5 Challenge Level: Challenge Level:1

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

Transformation ... or Not? link

Transformation ... or Not? 

Stage: 5 Challenge Level: Challenge Level:1

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