Recognizing features of functions

The  exercise appears under the Algebra II Math Mission. This exercise concentrates on properties of graphs in numerical and graphical forms.

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


 * 1) Choose which graph has the property: This problem provides a coordinate plane with three graphs and a condition. The student is asked to determine which of the graphs has the specific condition.Rfof1.png
 * 2) Choose which T-table has the property: This problem provides a T-table with three graphs and a condition. The student is asked to determine which of the graphs has the specific condition.Rfof2.png

Strategies
Knowledge of functional properties, terms and vocabulary are encouraged to ensure success on this exercise.
 * 1) Minimums and maximums are where the "bottom of the valley" or the "top of the hill" occurs.
 * 2) The period of a function is how long it takes until it begins to repeat.
 * 3) The end behavior of a graph are the limits as x approaches positive and negative infinity. The information on this exercise is always given in the positive direction first.
 * 4) An even function has the property f(-x)=x and has reflection symmetry over the y-axis. An odd function has the property f(-x)=-f(x) and has rotation symmetry about the origin.
 * 5) The x-intercepts occur when y=0 and the y-intercepts occur when x=0.

Real-life Applications

 * 1) Calculus describes how function change and experience with analysis of graphs will increase ability in calculus.