The "Dozen" Aspects of New Functions

For each new function that is introduced, mathematicians want to know about or how to do roughly a dozen things.
The "Dozen" Aspects of New Functions
1. define	Define the function in terms of something already known.
2. evaluate	Find values of the function used in expressions.
3. graph	Draw graphs involving the function with and without technology.
4. properties	Use the algebraic properties to simplify expressions.
5. proofs	Prove or derive particularly informative results.
6. limits	Take limits involving the function.
7. differentiate	Use the chain rule and implicit differentiation with the function.
8. integrate	Integrate indefinite and definite integrals.
9. tangent	Find the equation of the tangent line to a curve involving the function.
10. area	Find the exact area bounded by curves involving the function.
11. applications	Solve related rates, max/min and other applications with the function.
As you are introduced to each new function that we consider, analyze it against the list above.