Warm-up:

1. Warm-up:

2. Standard 2.2: determine and graph inverses of functions and identify symmetry in relations and functions [3-1, 3-4] In this lesson we will… • Discuss what symmetry is and the different types that exist. • Learn to determine symmetry in graphs. • Classify functions as even or odd.

3. What is Symmetry? • Point Symmetry: Symmetry about one point • Figure will spin about the point and land on itself in less than 360º.

4. Formal Definition: P’ M P

5. Symmetry to Origin: • This is the main point we look at for symmetry. • Let’s build some symmetry!

7. Determining Symmetry with Respect to the Origin

8. Let’s do a couple…

9. Line Symmetry

10. What’s that mean? U D

11. Lines We Are Interested In… • x-axis • y-axis • y = x • y = -x

12. x-axis

13. Example 3:

14. y-axis

15. Example 4:

16. y = x

17. y = -x

18. Example 5:

19. TOD: • What does it mean for a function to be symmetric to the line y = x? • How would one going about proving that symmetry mathematically?

20. Homework: • HW 2.2: P 134 #25 – 35 odd