[Math] Are unions, sums (…) of quasiconvex functions again quasiconvex

Question

for a project I need to prove quasiconvexity of several general functions. Can I argue that the union (or sum, or difference…) of quasiconvex functions is again quasiconvex?
I do know that the sum of convex functions is again convex, does this apply to quasiconvexity?

My functions may include the log-function, which is quasiconvex but not convex (for example).

Thank you very much for your help.

Best wishes,
Britta

Answer 1

Sum of two quasiconvex functions need not to be quasiconvex. Have you seen this http://en.wikipedia.org/wiki/Quasiconvex_function?