Thread: Continuosity

My Cal. 1 professor gave us this as an extra credit on one of our quizzes, however since no one got the correct answer, he didn't tell us how to find it.

Let "f" be a function defined by
x, if x is rational
f(x)=
-x, if x is irrational

Sketch the graph of this function as best you can and decide where is is continuos.

I'm not sure exactly how this graph would look, can anyone please help.

Originally Posted by ERiveraSr

My Cal. 1 professor gave us this as an extra credit on one of our quizzes, however since no one got the correct answer, he didn't tell us how to find it.

Let "f" be a function defined by
x, if x is rational
f(x)=
-x, if x is irrational

Sketch the graph of this function as best you can and decide where is is continuos.

I'm not sure exactly how this graph would look, can anyone please help.

this is similar to the Dirichlet function

maybe these will give you some ideas

see here

and here

and here