1. ## f(x)=1/x continuous?

Is f(x)=1/x considered continuous? A practice test I was doing said it was, but I figured it would have to be discontinuous at x=0. Does it possibly have to do with 0 not being in the domain? The simple definition of continuity given to me was if the graph could be drawn without picking up your pencil; this is why I do not see how 1/x can be continuous.

2. ## Re: f(x)=1/x continuous?

Originally Posted by Jzon758
Is f(x)=1/x considered continuous? A practice test I was doing said it was, but I figured it would have to be discontinuous at x=0. Does it possibly have to do with 0 not being in the domain? The simple definition of continuity given to me was if the graph could be drawn without picking up your pencil; this is why I do not see how 1/x can be continuous.
On what set? Not on $\displaystyle \mathbb{R}$. It is continuous on $\displaystyle (-\infty,0)\cup (0,\infty)$

3. ## Re: f(x)=1/x continuous?

$\displaystyle f(x) = \frac{1}{x}$ is continuous over its domain.

4. ## Re: f(x)=1/x continuous?

Okay good. I thought I was missing out on something regarding the definition of continuity. I think the practice test must be flawed. Thanks!