To graph, simply create a table of values for x and y (when x is __, y is __ ). Although if you know the basic parent function of ln(x), then this one is simply shifted to the left by three units.
For the domain, that means all values of x that satisfy the equation. Therefore, we have to know what values of x are invalid.
For logarithms, values of x must be positive and greater than zero. So we find the conditions that would violate it (what values of x would cause this to happen?):
x + 3 > 0
x > -3
So only values of x that are > -3 (but not equal to) would satisfy the equation. So the domain in interval notation is
The range are all the corresponding values of y, which begin at neg inf and go to pos inf (though very slowly, e.g., y = ln(1x10^100) = 230).
So the range is (-inf., +inf)
Use a graphing utility to see for yourself.