Prove that a continuous function of compact support defined on $R^n$ is bounded. I am working through a few sets of notes I found on the internet and I came across this exercise. How do I prove that a continuous function $f$ of compact support defined on $R^n$ is bounded?
It seems believable that it is true for $f$ in $R$ because I can visualize it but how do I prove this properly for $R^n$? Any ideas?

Put $K = {\rm supp}(|f|)$.  Since $K$ is compact and $|f|$ is continuous, then $\sup_{K} |f| < \infty$ and the supremum is attained on $K$.  Since $f$ is zero off $K$, we are done.
