# What is graph of graph of $y = (x-1)\sqrt{x}$

The book "A student's Guide to Fourier Transforms" 3rd edition, by J.F.James, published by C.U.P., on pages 20 and 21 quotes the equation $y = (x-1)\sqrt{x}$ as an example of one that does not meet the criteria for a Fourier transform because it is a two valued function. However the graph given is triple valued in places, with a continuous loop like that traced by an aeroplane looping the loop.

I cannot reconcile these, so please can anybody help with making sense of it, perhaps by showing what the plot of this equation really does look like?

The footnote or figure in the book is incorrect. The equation $(1 - y) (x^2 + y^2) = 2 x^2$ describes a graph similar to the figure in the book.
$y=(x-1)\sqrt x$ is nicely single valued if you view $y$ as a function of $x$. It is only defined for $x \ge 0$. It does have a vertical tangent at $x=0$. If you view $x$ as a function of $y$, it is double valued on $y \le 0, x \le 1$ A plot is below