each of these functions grows as x gets larger and larger. which function eventually exceeds the others…

Explanation:

Step1: Recall growth - rate of functions

Exponential functions grow faster than polynomial functions as (x\to\infty).

Step2: Identify function types

(f(x) = 3^{x}) is an exponential function, (g(x)=6.3x^{2}-5) is a quadratic (polynomial) function, and (h(x)=7x + 8.5) is a linear (polynomial) function.

Step3: Determine the fastest - growing function

As (x) gets larger and larger, the exponential function (f(x)=3^{x}) will eventually exceed the polynomial functions (g(x)) and (h(x)).

Answer:

(f(x)=3^{x})