Hello, advancedfunctions2010!
Your sketch is wrong . . .
For the function: .
a) Sketch the piecewise function
b) Determine the xvalues, if any, at which the function is discontinuous.
Find appropriate limits to support your conclusion. Code:
*  *
* 
*  *
*  *
*  *
* *
*
* 1
    + * +    
 *
 o

Obviously there is a discontinuity at
We verify this by taking the limit of "from both sides".
Take limit of as approaches 1 "from below".
. .
Take the limit of as approaches 1 "from above".
. .
Since the two limits are not equal, is discontinuous at
Edit: Too slow again . . . redundant explanation.
.