Continuity of Sums, Differences, and Constant Multiples - Expii

To prove continuity of linear combinations of functions, some helpful rules are: if f and g are continuous (at a point or on an interval), so are the sum f+g and difference f-g (at that point or on that interval); if f is continuous (at a point or on an interval), so is any constant multiple cf (at that point or on that interval).