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

both of these functions grow as x gets larger and larger. which function eventually exceeds the other?\n$f(x)=3^{x}-6$\n$g(x)=8x + 1$

both of these functions grow as x gets larger and larger. which function eventually exceeds the other?\n$f(x)=3^{x}-6$\n$g(x)=8x + 1$

Answer

Explanation:

Step1: Analyze growth - rate of functions

Exponential functions (y = a^x) ((a>1)) grow faster than linear functions (y = mx + b) as (x) approaches infinity. Here, (f(x)=3^x - 6) is an exponential - type function and (g(x)=8x + 1) is a linear function.

Step2: Consider the long - term behavior

As (x) gets larger and larger, the exponential function (3^x) will dominate the linear function (8x). The constant terms (-6) and (+1) do not affect the long - term growth rate of the functions.

Answer:

(f(x)=3^x - 6) eventually exceeds (g(x)=8x + 1) as (x) gets larger and larger.