I was surprised by the graph of $y=3+\ln(x+2)$:
I understand that $x=0 \implies y=3+\ln(2)$ and that $y=0 \implies x= e^{-3} -2$ and I derived this without problem. I was expecting the results to be different though. Considering the graph of $y=\ln(x)$ as a starting point, I was expecting the graph to translate 2 units to the left on the x-axis and 3 units up on the y-axis, sort of like with $f(x) = x^2$:
So my questions is, why does it translate up the extra $\ln(2)$ on the y-axis and less the $e^{-2}$ on the x-axis?
Thanks!