Example 2.9.  Show that the linear transformation    maps the right half plane    onto the upper half plane  .  

Explore Solution 2.9.

Enter the function  .  

Solve for the inverse function.

To solve for  ,   we use the following computations.

The solution is the upper half plane  .  Now use Mathematica to graph the transformation.

We see that the linear transformation    maps the right half plane    onto the upper half plane  .  

Another way of looking at the graphs:

(c) 2006 John H. Mathews, Russell W. Howell