I started learning continuity and uniform continuity but the textbook I am following does not provide any example after explaining the uniform continuity. I have a function $f:\mathbb{R}\rightarrow \mathbb{R}; f(x) = \sqrt{x^2+x+1}$, and I need to study its uniform continuity. Would be nice if you could walk me through the whole process of solving this, not just solving it for me. Thank you!