2 Reflection 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.
3 Reflection 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.
4 Line 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.
5 Examples of Lines of Symmetry Line of Symmetry Sample Artwork Example Shape
6 Examples of Lines of Symmetry Line of Symmetry Sample Artwork Example Shape
7 Even & Odd Functions Degree: highest exponent of the function Constants are considered to be even!Even degrees:Odd degrees:
8 Even Functions EVEN => All exponents are EVEN y-axis symmetry Example:y-axis symmetry
9 Odd FunctionsODD => All exponents are ODDExample:origin symmetry
10 NEITHER even nor odd NEITHER => Mix of even and odd exponents Examples:
11 Leading Coefficient (LC) The coefficient of the term with the highest exponent2 Cases:LC > 0LC < 0Agree?!?!
12 End 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!
13 Case #1: Even Degree, LC > 0 Example:Both ends go toward +∞
14 Case #2: Even Degree, LC < 0 Example:Both ends go toward -∞
24 Answer 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.