# Thread: Continuity of the Sawtooth Function.

1. ## 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.

2. ## Re: Continuity of the Sawtooth Function.

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)

3. ## Re: Continuity of the Sawtooth Function.

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.