what is the range of the function y = e^{4x}?\no y<0\no y>0\no y<4\no y>4

Explanation:

Step1: Recall the property of exponential function

The general form of an exponential function is $y = a^x$ where $a>0,a\neq1$. For the function $y = e^{4x}$, the base $a = e\approx2.718>0$.

Step2: Analyze the range

For any real - valued $x$, the exponential function $y = e^{u}$ (where $u = 4x$ and $u\in R$) is always positive. That is, $e^{4x}>0$ for all $x\in R$. There is no upper - bound for $e^{4x}$ as $x\rightarrow+\infty$, $e^{4x}\rightarrow+\infty$, and as $x\rightarrow-\infty$, $e^{4x}\rightarrow0$ but never reaches 0.

Answer:

B. $y > 0$