Modeling with combined functions

The  exercise appears under the Algebra II Math Mission. This exercise increases familiarity with operations on functions and complex multi-stage word problems.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the models: This problem has a context-driven story problem with several models that can combine. The student is expected to provide several different models with different inputs and outputs as specified in each line.Mwcombinedf1-p1.pngMwcombinedf1-p2.png

Strategies
Knowledge of some basic formulas, such as profit and distance, and familiarity with operations on functions are encouraged to ensure success on this exercise.
 * 1) The problems appears long, but it has just four parts:
 * 2) The first two parts are writing models of the two separate situations.
 * 3) The third part is writing how the two parts are related to each other.
 * 4) The fourth and final part is substituting 1) and 2) into 3).
 * 5) There is no need to simplify the model by distributing. It may be kept with parentheses.

Real-life Applications

 * 1) Exercises with the word "modeling" in them represent real-life situations and how to take the mathematics theory and apply it in meaningful ways to life.