Intersecting functions

The  exercise appears under the Algebra II Math Mission. This exercise helps to understand intersection of function via their T-tables and graphs.

Types of Problems
There are three types of problems in this exercise:


 * 1) Use the table to determine possible solutions: This problem provides a t-table for two functions and a collection of possible solutions. The student is asked to use the table to select all the options from the collection that could be the solution to the intersection of the functions.Intfun1.png
 * 2) Classify each input in the chart: This problem has graphs of two functions, labeled points, and a chart. The student is asked to determine which values are solutions to the individual equations, and to the intersection of the functions.Intfun2.png
 * 3) Approximate the solutions from the graphs: This problem has a graph of two functions. The student is asked to use the graph to approximate the solutions within 0.2 units.Intfun3.png

Strategies
Knowledge of the different views of a function are encouraged to ensure success on this exercise.
 * 1) On Use the table to determine the possible solutions the solution will occur in the interval where one function changes from being larger than the other to smaller, or vice versa.
 * 2) On Classify each input in the chart there generally seems to be one solution to each function's zeros, and two solutions to their intersection. Also, one answer is a "nothing."

Real-life Applications

 * 1) Situations with multiple constraints need to satisfy them simultaneous. Systems are a method of doing so.
 * 2) Often data collected through experimentation does not have a precise algebraic form. The strategies developed in this exercise can be used to analyze these type of situations.