Question

what is the range of the function y = 4e^x?
all real numbers greater than 0
all real numbers less than 0
all real numbers less than 4
all real numbers greater than 4

Explanation:

Step1: Recall the property of the exponential - function

The exponential function $y = e^{x}$ has a range of $(0,+\infty)$, that is, $e^{x}>0$ for all real - valued $x$.

Step2: Consider the given function $y = 4e^{x}$

Since $e^{x}>0$, when we multiply both sides of the inequality by 4 (a positive number), we get $4e^{x}>0$. So the range of the function $y = 4e^{x}$ is all real numbers greater than 0.

Answer:

A. all real numbers greater than 0