The parent function [tex]y=e^x[/tex] passes through the point [tex](0,1)[/tex], since [tex]e^0=1[/tex]
Your function passes through the point [tex](0,4)[/tex], 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 [tex]f(x)\mapsto f(x)+k[/tex]
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
[tex]y=e^x+3[/tex]
