Thread: A rational function is not continuous

Show that f is not continuous at x (see diagram).
ImageShack® - Online Photo and Video Hosting

Having trouble with this for a while, thanks..

Pick any rational x. Then f(x) is nonzero. There are irrational numbers arbitrarily near to x. Can you finish from there?

Edit: By the way, "rational function" is the name for a different kind of function from this one, namely one that is the quotient of two polynomials.

thanks, i read the proof regarding Q and R in my book, but i still dont really know how to answer it, any more tips? Thanks!

Write the definition of "f is continuous at x" (the one with epsilon and delta), then show that the definition does not hold for x rational, for the reason I gave. Try setting epsilon = f(x)/2.

thanks, i'll try it out..