Hello, Stuckasaurus!
I'm not sure what that third entry means.
It probably means that this graph is repeated over and over,
. . but I'll graph just one "cycle".
The brackets indicate intervals.
. . means: .
Brackets mean the endpoints are included.
If the endpoints are not included, parentheses are used.
. . means: .
And, yes, they can be "mixed".
. . means: .
This problem says:
If , the graph is a sine function: .
If , the graph is ... the xaxis.
The graph looks like this: Code:

1+ *
 * *
 * *
* *

  *        * * * * * * * * *  
 2 4
This function says:
If is between 1 and 0, the graph is , the xaxis.
If is an integer, the graph is ½.
If is between 0 and 1, the graph is
And the graph looks like this: Code:

1o=======o

*

  o=======o    +  
1  1