Modeling with composite 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 are two types of problems in this exercise:


 * 1) Find the model: This problem provides a context-driven situation involving composition of two other models. The student is expected to correct write the function that can be used to model the overall situation.Mwcompositef1.png
 * 2) Select the models that represent the situations: This problems reports several models of different situations. The student is asked to select which compositions can be created to model particular questions and indicate the correct selection in the chart.Mwcompositef2.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) Making a chart and describing the inputs and outputs in words can assist understanding which is the "inside" function and which is the "outside" function.
 * 2) There is no need to simplify the model by distributing. It may be kept with parentheses.
 * 3) For the second type of problem, there tends to be one selection under each column.

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.