Intermediate Value Property on a uniformly continuous function

Question

Is a uniformly continuous function on [a,\infty) consume Intermediate Value Property?

Answer 1

A uniformly continuous function is continuous. Consequently, since you have a continuous function in a closed set, you can apply the Intermediate Value Theorem.

Answer 2

You can treat limits at both infinities, say $\lim_{x\to\infty}f(x)$ as a point, and apply IVT.