Rate of Growth precise definition for function

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Could give me precise definition in simple english what really Rate of Growth means when we talking about some function T(n)? And how should I denoted it?

As I understand, if we have a functions like:

$$T1(n) = 6*n^2 + 5*n + 123$$ $$T2(n) = 2^n + 3*n^2 + 7 * n! + 5*n$$

Then, Rate of Growth will be equal to (I don't know how to denote it):

$$ T1RateOfGrowth = n^2 $$ $$ T2RateOfGrowth = n! $$