Question

What is the range of the function y=e^4x? y<0 y>0 y<4 y>4

Answer 1

We have been given the function $y=e^{4x}$

We know that the range is set of y values for which the function is defined. Therefore, we will find the value for x and then observe the restriction is y's values.

$y=e^{4x}\\\ln y = \ln (e^{4x})\\\ln y =4x\\x=\frac{1}{4}\ln y$

Now, we know that logarithm function is not defined for negative values. Hence, the value for y is always greater than zero.

Therefore, the range of the function is given by y>0

B is the correct option.

Answer 2

This exponential function is increasing .

Whatever the value of x, y is always positive. So the range of y is all value greater than 0==> y>0