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

Answer:

B. $y > 0$

Explanation:

Step1: Consider the 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 value of $x$, the exponential function $y = e^{4x}$ will always be positive. As $x\to-\infty$, $y = e^{4x}\to0$ (but never reaches 0), and as $x\to+\infty$, $y = e^{4x}\to+\infty$. So the range of the function $y = e^{4x}$ is $y>0$.