# A Problem About Uniformly Continuous functions

1. Sep 20, 2008

### herbyoung

Let I be the interval I=[0,infinity). Let f: I to R be uniformly continuous. Show there exist positive constants A and B such that |f(x)|<=Ax+B for all x that belongs to I.

2. Sep 20, 2008

### mathwonk

what is the definition of uniformly continuous? state it in terms of delta x and delta y.

3. Sep 20, 2008

### herbyoung

I have known the answer. Thanks.