Question

Fix m, b ∈ R with m > 0 (for convenience). Define f(x) = mx + b for all x ∈ R. Then f : R → R is a function whose graph is a line. Prove that f is uniformly continuous from the definition. (Hint: If this looks too daunting, try this with m = 2 and b = 1. If you succeed with these numbers you can erase them and replace them with m and b.) this is a calculus analysis course