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

each of these functions grows as x gets larger and larger. which function eventually exceeds the others? f(x) = 4^x - 2 g(x) = 3x^2 - 2x - 4 h(x) = 8x

each of these functions grows as x gets larger and larger. which function eventually exceeds the others? f(x) = 4^x - 2 g(x) = 3x^2 - 2x - 4 h(x) = 8x

Answer

Explanation:

Step1: Recall growth - rate of functions

Exponential functions (a^x) ((a>1)) grow faster than polynomial functions (b_nx^n + b_{n - 1}x^{n - 1}+\cdots+b_1x + b_0) ((n\geq0)) and linear functions (cx) ((c>0)) as (x\to+\infty).

Step2: Identify function types

(f(x)=4^{x - 2}=\frac{4^x}{16}) is an exponential function with base (a = 4>1). (g(x)=3x^2-2x - 4) is a polynomial function of degree (n = 2). (h(x)=8x) is a linear function.

Answer:

(f(x)=4^{x - 2})