Math Assistance

I need help with functions and logarithms (yes, I know they're algebra level math...)

I'm being asked to graph a function of the form:
a log (x + b) + c

I know that "a" is just an exponent you add to the log, but I'm not sure whether I should be setting "(x + b)" to the power of "a", or if I should be setting "(x + b) + c" to the power of "a". Furthermore, I shouldn't be using any decimals when I graph, I'm supposed to simplify the answer with euler's number. I know what euler's number is, but I've never been asked to graph (or even simply an answer) with it before, so I'm a little lost.
BTW, the graphing is done with a computer program, which is why it is able to plot Euler's...

It also wants to know the asymptotes of the function, and again, I am not sure how to find out the asymptotes of logarithms.

if f(x) = a * log(x + b) + c, then c just shifts the graph in the vertical direction

verticle asymptote at -b because you can't take the log of a negative number