Question

1. submit answer practice similar attempt 1: 10 attempts remaining. which of the following best describes the shape of the graph of $e^{x}$? a. it decreases toward zero as $x$ increases. b. it increases rapidly and is always above the $x$-axis. c. it starts at $-\infty$ and increases to $+\infty$. d. it increases from zero to a maximum point and then decreases.

Explanation:

The function $y = e^{x}$ is an exponential - growth function. Its derivative $y'=e^{x}>0$ for all real - valued $x$, so it is always increasing. Also, $e^{x}>0$ for all $x\in R$ since the exponential function with base $e\approx2.718$ is always positive.

Answer:

B. It increases rapidly and is always above the $x$-axis.