Question

The graph of y= e^x is transformed as showed in the graph below. Which equation represents the transformed equation

Answer 1

The parent function $y=e^x$ passes through the point $(0,1)$, since $e^0=1$

Your function passes through the point $(0,4)$, which means that the parent function has been translated 3 units up.

To translate a function vertically, you have to add a constant, i.e. you have to transform $f(x)\mapsto f(x)+k$

k is the amount of units you want to translate: positive if you translate upwards, negative if you translate downwards.

In your case, you move 3 units upwards, so you want k=3 and your function is

$y=e^x+3$