Question

what is the range of the function y = e^{4x}?
o y<0
o y>0
o y<4
o y>4

Explanation:

Step1: Recall exponential - function property

The general form of an exponential function is $y = a^{x}$, where $a>0,a
eq1$. For the function $y = e^{4x}$, the base of the exponential function is $e\approx2.718>0$.

Step2: Analyze the range of exponential function

For any real - valued exponent $u = 4x$ (where $x\in R$), the exponential function $y = e^{u}$ always gives a positive output. That is, $e^{u}>0$ for all $u\in R$. Since $u = 4x$ and $x$ can be any real number, $y=e^{4x}>0$. So the range of the function $y = e^{4x}$ is $y>0$.

Answer:

B. $y>0$