Disclaimer: This is a question from an exam that I have already taken and has already been graded.

Here’s the question: Find the domain and range of g(x) = A cot(x-C) + D.

I put “all real numbers” for both and got domain wrong (range was right obviously). Taking the test, I thought hard about this. I reasoned that we don’t know what C is. Because the domain is defined as all the possible x values, I deduced therefore that x can be any numerical value.

The way I was looking at it, the graph g(x) = cot (x) has asymptotes at 0, pi, 2pi, etc. However, the graph of g(x) = cot(x+pi/2) has asymptotes at pi/2, 3pi/2, etc. Therefore, and this is the thrust of my argument, * X can take on any value*.

When I asked my professor, he told me that C is a parameter, not a variable. When I asked him for a value that X could not be, he said “C.” Now, I understand that I am wrong here, and other people wanted to talk to him so I just walked away. But I’m still not satisfied. I still believe that there is no real number that X could not be.

Can anyone shine some light on this for me?