A projective real hyperelliptic curve
As some alert readers pointed out, I managed to overlook making a graph of a projective real hyperelliptic curve. To correct this oversight, here's what they look like. As before, the red curve shows where z = 0 and the blue is the hyperelliptic curve y2 = x6 + x2 + x. These graphs may also give some insight into of one of the complications involved in using these types of curves: that fact that they have two points at infinity instead of just one.