What topics are usually covered in Algebra II (in high school)?

I have been teaching at a university for 20 years in the "math development" program. Over the last 20 years we have been averaging around 250 students per semester in about 20 or sections of three math classed 090, 091, and 092. These classes get the students ready for the typical math found in science and business classes (most majors require at least one math class past the 092). I have taught all three of the classes that I mentioned and the three topics that you described in on all or some of the syllabuses. So yes it is surprising that high school graduated have never seen some of the topics that you defined, but indeed it is common.... On the other hand is is very frustrating when I have trouble explaining to a student that (-4) + 9 = 5... let alone -3 - (-4) = 7

Yes, but they may not have done well in the class or just may have forgotten what they learned. I took Algebra II in high school but I came out of it with a C, barely. After about 10 years I took College Algebra and thankfully remembered the basics, but for some things I just had no clue. Logarithms, for example, I remember covering them in high school but couldn't remember anything when we started the topic in College Algebra. That's just my personal experience of course, but those topics should definitely be covered in any algebra II class if not earlier.

Yes, but they may not have done well in the class or just may have forgotten what they learned. I took Algebra II in high school but I came out of it with a C, barely. After about 10 years I took College Algebra and thankfully remembered the basics, but for some things I just had no clue. Logarithms, for example, I remember covering them in high school but couldn't remember anything when we started the topic in College Algebra. That's just my personal experience of course, but those topics should definitely be covered in any algebra II class if not earlier.