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 exponential - function property

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 of the exponential function

For any real - number $x$, the value of $e^{4x}$ is always positive. As $x\to-\infty$, $e^{4x}\to0$ (but never reaches 0), and as $x\to+\infty$, $e^{4x}\to+\infty$.

Answer:

B. $y > 0$