both of these functions grow as x gets larger and larger. which function eventually exceeds the…

Explanation:

Step1: Analyze the growth rate of polynomial and exponential functions

For a polynomial function (f(x)=2.2x^{2}-2x + 5), its degree is (n = 2). The general form of a polynomial function is (y=a_{n}x^{n}+a_{n - 1}x^{n-1}+\cdots+a_{1}x + a_{0}), and its growth rate is determined by the leading term (a_{n}x^{n}) as (x\to+\infty). For an exponential function (g(x)=2.2^{x}), the general form is (y = a^{x}(a>1)).

Step2: Recall the growth - rate comparison theorem

According to the growth - rate comparison of functions: For any positive real numbers (a) ((a>1)) and (n) (where (n) is a positive integer), (\lim_{x\rightarrow+\infty}\frac{x^{n}}{a^{x}}=0). Let (a = 2.2) and (n = 2). As (x\to+\infty), we can use the fact that exponential functions (y=a^{x}(a > 1)) grow faster than polynomial functions (y = b_{n}x^{n}+b_{n-1}x^{n - 1}+\cdots+b_{1}x + b_{0}(n\in N,b_{n}\neq0)).

Answer:

The function (g(x)=2.2^{x}) eventually exceeds the function (f(x)=2.2x^{2}-2x + 5).