Monotonic transformation

[RS]

Please discuss. Give reasons
Which of the following are monotonic transformations? (1) u = 2v −13;
(2) u = −1/v^2; (3) u = 1/v^2; (4) u = lnv; (5) u = −e^−v; (6) u = v^2;
(7) u = v^2 for v > 0; (8) u = v^2 for v < 0.

[hoouin]

find du/dv and see if it is positive. i.e

du/dv  >0

e.g for i) du/dv=2>0  hence it is monotonic transformation.