For info, two different terms seem to be tangled up here:
'auto-zoom' and 'auto-focus'.
'Auto-focus' is all about finding focus - the lens and camera automatically work together to make a sharp picture, once you point the lens towards the subject you want to photograph, and press the shutter button on the camera.
'Auto-zoom' usually relates to lenses that can enlarge or reduce the image in your viewfinder (or rear display) with a push of a button on the camera or lens, or sometimes even by automatically zooming in on a subject or face for you. However, with a lens like the 50-200 on the K-x, you need to do the zooming manually by turning the zoom ring on the lens by hand.
There's a lot of good information about autofocus, and other photography concepts, in the tutorials below:
Digital Photography Tutorials