The answer is:
The first option shows the graph of the given function.
<h2>Why?</h2>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:
Finding the y-axis intercept, we need to make "x" equal to 0, so:
We need to remember that any number elevated or powered to 0 is equal to 1, so:
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:
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.
