Let f(x)=
x2−3, for x<3,
x2+3, for x≥3

I need to determine the total variation and the quadratic variation of f(x) on the interval [−4, 4].

For the total variation, I guess I can use my raw way to do it. It means see that f(−4)=13, f(0)=−3, f(2.999999)=5.99999, f(3)=12, f(4)=19.

So I could say that the total variation is (13−(−3))+(5.999999−(−3)+(19−12) ? Or should I take into account the jump between f(2.999999) and f(3) and if yes how ?