Images of Regions Under Cayley's Transformation I'm working on the following problem for my complex analysis course:

Problem $\bf 1$: Find the images of the followings under the Cayley's transformation:  $a)$ imaginary axis  $b)$ real axis  $c)$ upper half plane  $d)$ horizontal line through $i$

I can't seem to find Cayley's transformation anywhere in our textbook - could someone clarify to me what it is? I've done a Google search and have found mixed results.
Furthermore, how can I go about finding this image for each part? Like for this first part, should I just consider a complex number $z = ai$, see what it is mapped to, and then try to establish a general pattern?
Any help is greatly appreciated!

For the image of the imaginary axis under the Cayley's transformation:  $$0 + yi\mapsto\frac{yi - i}{yi + i} = \frac{y - 1}{y + 1}\:\text{ ( the real-axis ) }$$
The map for the real-axis:  $$x + 0i\mapsto\frac{x - i}{x + i}\:\text{ ( Note $\rvert\frac{x - i}{x + i}\rvert = \rvert\frac{\overline{x + i}}{x + i}\rvert = 1$, so this is the unit circle centered at the origin. ) }$$
