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

both of these functions grow as x gets larger and larger. which function eventually exceeds the other? f(x)=x² + x + 8 g(x)=4^(x - 3)+9

both of these functions grow as x gets larger and larger. which function eventually exceeds the other? f(x)=x² + x + 8 g(x)=4^(x - 3)+9

Answer

Explanation:

Step1: Analyze function types

$f(x)=x^{2}+x + 8$ is a polynomial function of degree 2. $g(x)=4^{x - 3}+9$ is an exponential function.

Step2: Recall growth - rate of functions

Exponential functions ($y = a^{x}$, $a>1$) grow faster than polynomial functions as $x$ approaches infinity. Here, for $g(x)=4^{x - 3}+9$, the base of the exponential part $a = 4>1$.

Answer:

$g(x)$ eventually exceeds $f(x)$.