# Math Help - uniform continuity proof

1. ## uniform continuity proof

Suppose that f:R-->R is continuous and has the property that for every epsilon>0, there is M>0 such that if abs(x)>=M, then abs(f(x))<epsilon. Show that f is uniformly continuos.

2. Is this true? take $f(x)= \frac{1}{x}$

3. The given function by Jose27 is not continuous.
There are a lot of threads of similar questions. Observe that in $[-M,M]$ a continuos function is always uniformly continuous and apply the condition for $\varepsilon/2$.