Investigate whether:
1. An even function plus an even function is an even function, or odd function, or neither.
2. An even function plus an odd function is an even function, or odd function, or neither.
3. An odd function plus an odd function is an even function, or odd function, or neither.
4. An even function times an even function is an even function, or odd function, or neither.
5. An even function times an odd function is an even function, or odd function, or neither.
6. An odd function times an odd function is an even function, or odd function, or neither.