b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

Students should be able to recognize the basic function types (linear, quadratic, polynomial, root, rational, exponential, and so on) by graph and by equation. If they aren't comfortable with these functions, mixing them together will make a lumpy and awkward-looking mishmash of functions instead of the tasty mathematical smoothie they should get.

As far as combining functions goes, students should feel comfortable adding, subtracting, multiplying, and dividing. For instance, students should be aware that dividing a polynomial function by a linear function will give us a rational function. They should also be aware of these different function types in relation to different contexts and how these contexts do or don't change the function types and how.