# Continuity of the Sawtooth Function.

• Sep 15th 2011, 02:49 PM
riddikulus
Continuity of the Sawtooth Function.
Sawtooth function: Draw the graph of f(x) = x - [x]. At which points is f discontinuous? Is it left- or right-continuous at those points?

I have no idea where to begin...when I graphed this, it said it was undefined everywhere.
• Sep 15th 2011, 03:31 PM
skeeter
Re: Continuity of the Sawtooth Function.
Quote:

Originally Posted by riddikulus
Sawtooth function: Draw the graph of f(x) = x - [x]. At which points is f discontinuous? Is it left- or right-continuous at those points?

I have no idea where to begin...when I graphed this, it said it was undefined everywhere.

attached graph ... note the function is defined at (1,0)
• Sep 15th 2011, 03:36 PM
Plato
Re: Continuity of the Sawtooth Function.
Quote:

Originally Posted by riddikulus
Sawtooth function: Draw the graph of f(x) = x - [x]. At which points is f discontinuous? Is it left- or right-continuous at those points?

What is important here is for you to realize that
$\displaystyle x-[x]\in [0,1).$

Thus the graph has a range $\displaystyle [0,1).$

So do the question.