2Reflection SymmetryReflection Symmetry (sometimes called Line Symmetry or Mirror Symmetry) is easy to recognize, because one half is the reflection of the other half.Here is a dog. Her face made perfectly symmetrical with a bit of photo magic.The white line down the center is the Line of Symmetry.
3Reflection SymmetryThe reflection in this lake also has symmetry, but in this case:the Line of Symmetry is the horizonit is not perfect symmetry, because the image is changed a little by the lake surface.
4Line of SymmetryThe Line of Symmetry (also called the Mirror Line) does not have to be up-down or left-right, it can be in any direction.~But there are four common directions, and they are named for the line they make on the standard XY graph.
5Examples of Lines of Symmetry Line of Symmetry Sample Artwork Example Shape
6Examples of Lines of Symmetry Line of Symmetry Sample Artwork Example Shape
7Even & Odd Functions Degree: highest exponent of the function Constants are considered to be even!Even degrees:Odd degrees:
8Even Functions EVEN => All exponents are EVEN y-axis symmetry Example:y-axis symmetry
9Odd FunctionsODD => All exponents are ODDExample:origin symmetry
10NEITHER even nor odd NEITHER => Mix of even and odd exponents Examples:
11Leading Coefficient (LC) The coefficient of the term with the highest exponent2 Cases:LC > 0LC < 0Agree?!?!
12End Behavior What happens to f(x) or y as x approaches -∞ and +∞ We can figure this out quickly by the two things we’ve already discussedDegree of function (even or odd)Leading coefficient (LC)Let’s look at our 4 cases…jot these down in your graphic organizer!
13Case #1: Even Degree, LC > 0 Example:Both ends go toward +∞
14Case #2: Even Degree, LC < 0 Example:Both ends go toward -∞
24Answer the following: (submit these answers in the assignment drop box) 11. Explain how you know a functionis even, odd, or neither when you are looking at the graph? (like in questions 1-4)12. Explain how you know a functionis even, odd, or neither when you are looking at the equation? (like in questions 5-10)13. Write an even function.14. Write an odd function.15. Write a function that is neither.