Are decision tree algorithms linear or nonlinear
A decision tree is a non-linear mapping of X to y. This is easy to see if you take an arbitrary function and create a tree to its maximum depth.

For example:

if x = 1, y = 1
if x = 2, y = 15
if x = 3, y = 3
if x = 4, y = 27
...


Of course, this is a completely over-fit tree and won't generalize. But it demonstrates why a decision tree is a non-linear mapping.