Is there a name for family of these "well behaved" functions.

Question

I am looking for right nomenclature for functions that exhibit following two properties

1. $\max f(x_1,\cdots,x_n)<\infty$
2. $f(x_1,\cdots,x_n)\rightarrow 0 \quad \text{as}\quad x_i>N_i, \quad \forall \quad N_i\in R$

Gaussian function is one such function. Can someone add more examples to the list. And more importantly what do we call them collectively.