Things you might have noticed

Underneath are some unusual looking graphs. Try to describe each graph in words. What features do you notice?

How did you describe the features of the graphs? Did you use mathematical language to help you?

Did you use shapes or equations to describe different sections?

If you did this in a group, were certain graphs drawn more accurately than others? If so, what was different about the way they were described?

This function is made up of sections of the form \(y=a\). Were equations used in the description?

What is the value of the function when \(x=1\)? How did you interpret the closed and open circles at the end of the sections? Where have you seen these used before?

The middle section of this function is interesting. It is made of sections of \(y=2x\) and \(y=−2x\), but can you think of another way you could describe it?

What happens at the points (3,0) and (8,0)? Which line would you define as them being part of?

There are two features here that have not occured in the other graphs. We have a non-linear section, and our function continues as \(x\) gets larger.

These are all graphs of piecewise functions. The whole function \(f(x)\) is made up of differing sections (or pieces).

Now you have described and sketched the functions, can you write their equations? The way they were described might help you with this. You can check your answers in the taking it further section.