Diodes circuit exercise
I would recommend simulating this kind of problem to get an understanding. Then you can look at the voltages at different points in the circuit, see the current flows and easily insert different test voltages.

I knocked together a simulation in Paul Falstad's circuit simulator applet: http://www.falstad.com/circuit/. It's pretty quick and easy for simple circuits but doesn't have the power of a proper SPICE simulator.

Here's the circuit in the simulator.

The graphical output (with 1V per grid square on the scope) looks like this:


The left hand graph at the bottom is the input function (in this case at 50Hz) and the right hand graph is the output function. You can see that the curve is the same when the input is between +-5V, but different (half the amplitude, but shifted up or down to make the function continuous) outside of these values.