y = 3√[(16-x^2)/(2x+17)] and y = -3√[(16-x^2)/(2x+17)] what’s this ?

what is this?

What a funny question! We can first do a study of the two associated functions.

We are told that the domain of definition of both functions is ]-∞ ;-17/2[ U [-4 ;4] and that the tables of variations are those on the left side (we can see here the differences, translated into “symmetries”, due to the minus sign).

But we still do not have a clear explanation! Let’s have a look at each curve.

They are both conforming to the previous tables of variations. It is possible to notice the horizontal tangents (and the symmetries already observed).

Let’s concentrate on the portion of curves from the interval [-4 ;4] and put them together on a unique graph.