Question

Which of the following shows the graph of y=2e^x

Answer 1

Hello!

The answer is:

The first option shows the graph of the given function.

Why?

Since the given function is an exponential function, we are looking for an exponential function graph, with a function that intercepts the y-axis at y equal to 2, or the point (0,2).

So, since we are given just one exponential graph, let's find the y-axis intercept in order to assure that the correct option is the first graph.

The function is:

$y=2e^{x}$

Finding the y-axis intercept, we need to make "x" equal to 0, so:

$y=2e^{0}$

We need to remember that any number elevated or powered to 0 is equal to 1, so:

$y=2*1=2$

We have that the function intercepts the y-axis at y equal to 2, or the point (0,2).

Finding the x-axis intercept, we need to make "y" equal to 0, so:

$y=2e^{x}$

$0=2e^{x}$

$Ln(0)=Ln(2e^{x})$

Now, since the natural logarithm of "0" does not exist in the real numbers, we can see that there is not x-axis intercept for this function.

Hence, the first option shows the graph of the given function.

Have a nice day!

Note: I have attached a picture for better understanding.