And that was mentioned in the discussion earlier on this thread, right? Also note that your graph of the log function is way way too low resolution to be useful for our current purposes. We are only concerned about the domain of the function between 0 and 1, because the h() values are sigmoid outputs. Also note that you are graphing log_{10}, but we are using natural logs here. The fundamental shape of the curve between 0 and 1 is the same though.
Here’s a better version of the graph of the natural log function showing only the domain we care about:
That graph is from this other thread which discusses basically the same point.