increasing functions consider the graph shown, which function eventually exceeds the other functions? a y =…

increasing functions consider the graph shown, which function eventually exceeds the other functions? a y = 2^x b y = x^2 c y = 2x d cannot be determined which function will eventually surpass the other functions? a y = x^100 b y = 100x c y = 100^x d y = x^100 + 100x

increasing functions consider the graph shown, which function eventually exceeds the other functions? a y = 2^x b y = x^2 c y = 2x d cannot be determined which function will eventually surpass the other functions? a y = x^100 b y = 100x c y = 100^x d y = x^100 + 100x

Answer

Explanation:

Step1: Recall growth - rate of functions

Exponential functions with a base greater than 1 grow faster than polynomial and linear functions as (x) approaches infinity.

Step2: Analyze first set of functions

For (y = 2^x) (exponential), (y=x^2) (polynomial) and (y = 2x) (linear), as (x) gets large, the exponential function (y = 2^x) will eventually exceed the other two.

Step3: Analyze second set of functions

For (y=x^{100}) (polynomial), (y = 100x) (linear), (y=100^x) (exponential) and (y=x^{100}+100x) (polynomial), the exponential function (y = 100^x) will eventually exceed the other three as (x) approaches infinity.

Answer:

First question: A. (y = 2^x) Second question: C. (y = 100^x)