Natural Logarithmic Functions
The function
y = log(x+b)
is graphed for b from -4 to +4. Watch the verticle asymptote
or pole shift with the value of b.
Operating within the function gives an x-translation.
The function below is
y = a log(x+2)
and is plotted for b from -1 to +1.
Recall that multiplying a function by a constant scales the y direction
with negative scaling including a reflection.