Determine if a function is uniformly continuous by looking at its graph? Today my professor introduced the idea of uniform continuity. However, I had difficulty visualizing what the graphical interpretation of a function being uniformly continuous is. Is it possible to determine if a function is uniformly continuous by looking at its graph?

Can anyone give an intuitive interpretation of uniform continuity?
Generally it is impossible to judge whether a function is uniformly continuous only by looking at the graph. 

Note that even differentiable uniformly continuous functions can have unbounded derivatives (namely unbounded slopes). One immediate example is $f(x)=x\sin(1/x)$ on $(0,1]$, see here for a proof. 

Of course, if defined on a compact set (say a bounded closed interval) then it trivially suffices to check whether the function is continuous. 

As far as I can tell, I can't find a good intuitive interpretation of uniform continuity.
Yes, the slopes of the tangents are bounded. At least if you are dealing with a differentiable function, but this gives you the intuition.