Let's say a function f(x) has Property A if f(x·k) = k·f(x) for all numbers k (and all inputs x where the function is defined on xk) Let's say a function f(x) has Property B if f(x+k) = f(x) + kC for all numbers k (where C is a fixed constant)
[Reminder: g(2·x) is not the same thing as 2·g(x) For example try g(x)=3x+5] Directions:

1. Investigate property A and property B
2. List some functions which satisfy property A
3. List some functions which no not satisfy property A
4. List some functions which satisfy property B
5. List some functions which no not satisfy property B
6. Are there functions which satisfy both properties?
7. Are there functions which satisfy property A but not property B? If so, which. If not, why not.
8. Are there functions which satisfy property B but not property A? If so, which. If not, why not.
9. Use tables, formulas, graphs, "difference tables", and full English sentences which
              qualitatively but precisely describe the phenomena you are seeing.
10. Give a paragraph conclusion/summary of what you have learned.

    Scratchwork (what you put into your portfolio should be
    an organized exposition; below is just work space):