Perhaps I haven't had enough coffee... is there a bug in the graph app relative to (for example) #x^3/(x+1)#? I don't see why there should be that parabolic looking bit in Q II.

I have a feeling that this is more of a math problem than an actual bug.

Try plotting that function on any other online graph calculator, you'll get the exact same curve.

For example, let's say that #x = 3#. This will get you

#y = 3^3/(3 + 1) = 27/4#

But for

#y = 27/4 = x^3/(x+1)#

you also get

#4x^3 - 27x - 27 = 0#

This will produce

#{ (x_1 = 3), (x_(2,3) = - 1.5) :}#

The vertex of that parabolic thing lies at #(-3/2, 27/4)#, so I guess that makes sense after all.