What happens in a graph when you modify the value of $a$ in the following equation:
$ae^x$ where e is the natural number.
At first it seemed like it was translating the graph horizontally but when $a$ is negative it inverses the graph. I then thought it was dilating the graph however it didn't look like the curve between the horizontal and vertical asymptote was changing, it was just moving horizontally. So how would i describe this change?
The fun thing about the exponential function is that stretching the graph vertically and translating it horizontally yield the same result. To be precise: $$a\cdot e^x=e^{x+b}\quad\text{where $a=e^b$.}$$ On the left: Stretch the graph vertically by a factor $a$. On the right: Translate it left a distance $b$.
Exercise: Figure out the analogous phenomenon on the graph of the logarithm.