Determine if a function is even or odd from its graph

The  exercise appears under the Algebra II Math Mission. This exercise classifies functions as even or odd (or neither).

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


 * 1) Determine if the rule is an even or odd function: This problem provides a rule for a function as f(x). The student is asked to determine if the given function is even or odd.Eaof1.png
 * 2) Determine if the graph is an even or odd function: This problem provides the graph of a function. The student is asked to determine if the given function is even or odd.Eaof2.png

Strategies
Knowledge of functional transformations and properties of even and odd functions are encouraged to ensure success on this exercise.
 * 1) Even functions have reflection symmetry over the y-axis. Also, $$f(-x)=f(x)$$.
 * 2) Odd functions have rotation symmetry about the origin. Also, $$f(-x)=-f(x)$$.
 * 3) Generally for polynomials, functions are even if their degrees are even and they are odd if their degrees are odd. Constants are even degree.

Real-life Applications

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