Given a colloquial definition of uniform continuity as $f(x)$ and $f(y)$ can be made to be arbitrarily close when $x$ and $y$ are sufficiently close, and the distance between $x$ and $y$ is independent of $x$ and $y$.
I'm not really sure how to picture a uniformly continuous function in my head. I showed that if the derivative of a function is bounded, then it will be uniform continuous. (I had trouble with the converse though.) Thinking along the lines that I need to bound the change in $f$.
How do you visualize uniform continuity?