Decision boundary of a decision tree:

A) Is always a straight line/hyperplane in the variable space

B) can have any shape: decision trees can represent precisely any complex decision boundary curve (e.g. predict "class 1" whenX²₁ +X⁴₂>0

X12+X24>0, "class 0" otherwise)

C) Idividualsplits are performed on one variable at a time only, so the boundaries of individual regions are always aligned with some axis in the variable space, but we have multiple regions, hierarchically embedded into each other, so the resulting boundary can provide a good piecewise-linear approximation to some more complex shape.

D) Is quadratic, e.g. any curve with functional form that involves up to 2nd degrees of the predictor variables can be represented exactly.