Question

1. label the graphs as $f(x)$ or $g(x)$. $f(x)e^{x}$ and $g(x)e^{4x}$

a:
b:
a. $g(x)$
b. $f(x)$

Explanation:

Exponential functions $f(x)=e^{kx}$ grow faster as $k$ increases. For $x>0$, $4x > x$, so $e^{4x}$ is larger than $e^x$ at the same positive $x$-value. Graph A is higher for positive $x$, matching $e^{4x}$. Graph B is lower for positive $x$, matching $e^x$.

Answer:

A: $g(x)=e^{4x}$
B: $f(x)=e^{x}$