I want to know why the following three graphs include the line y = x?

(1) g(x) = x + [4/(x^2+1)

(2) f(x) = (x^2+1)/x

(3) y = (x^2-6x+12)/(x-4)

I am trying to learn curve sketching from my single variable calculus textbook. I am not asking you to graph all three. I just want to know why the above functions include the line y = x as part of the graph.