Warm-Up

1. Warm-Up • Analyze the graph below. List the zeros, domain, range, any intervals of change, relative max/ min. • Are the following functions polynomial functions? Explain • Determine the end behavior of “a” in the previous problem. • Write the following polynomial in standard form and determine the end behavior. • Determine if the function above has even, odd, or neither symmetry. • Describe the symmetry of (even, odd, neither). Explain. • Use synthetic substitution to evaluate the following function when x= -3

2. Group Time!!! In groups of 4, complete the review sheet. Make sure that each problem is completed as each group will have the opportunity to present 1 or more problems. We will use random selection to chose problems. Use your interactive notebook, notes and any HW quizzes to help you. I am here as a guide and will not be giving any answers. Please have notes present if you ask me questions. Correct answers will earn each team member ½ a point on their test.

3. Warm-Up List any intervals of decrease/ increase or constant. The function is: -decreasing on the interval -increasing on the interval -decreasing on the interval -increasing on the interval

4. Notes Over 2.3 Increasing and Decreasing Functions Determining Relative Maximum or Minimum. Relative Maximum Relative Minimum *The highest or lowest point in a particular section of a graph.

5. Identify the relative maximum and minimum.

6. WARM UP Zeros: Domain: Range: Relative Maximum: Relative Minimum: Intervals of Increase: Intervals of Decrease:

7. Symmetry Essential Question: How do you determine the shape and symmetry of the graph by the polynomial equation?

8. Even, Odd, or Neither Functions • Not to be confused with End behavior • To determine End Behavior, we check to see if the leading degree is even or odd • With Functions, we are determining symmetry (if the entire function is even, odd, or neither)

9. Even and Odd Functions (algebraically) A function is even if f(-x) = f(x) If you plug in x and -x and get the same solution, then it’s even. Also: It is symmetrical over the y-axis. A function is odd if f(-x) = -f(x) If you plug in x and -x and get opposite solutions, then it’s odd. Also: It is symmetrical over the origin

10. Even Function Y – Axis SymmetryFold the y-axis (x, y)  (-x, y) (x, y)  (-x, y)

11. Test for an Even Function • A function y = f(x) is even if , for each x in the domain of f. f(-x) = f(x) Symmetry with respect to the y-axis

12. Symmetry with respect to the origin (x, y)  (-x, -y) (2, 2)  (-2, -2) (1, -2)  (-1, 2) Odd Function

13. Test for an Odd Function • A function y = f(x) is odd if , for each x in the domain of f. f(-x) = -f(x) Symmetry with respect to the Origin

14. Even, Odd or Neither? Ex. 1 Graphically Algebraically EVEN

15. Even, Odd or Neither? Ex. 2 Graphically Algebraically ODD

16. A negative # raised to an odd power is negativeA negative # raised to an even power is positive

17. Ex. 3 Even, Odd or Neither? Graphically Algebraically EVEN

18. Ex. 4 Even, Odd or Neither? Graphically Algebraically Neither

19. Even, Odd or Neither? EVEN ODD

20. What do you notice about the graphs of even functions? Even functions are symmetric about the y-axis

21. What do you notice about the graphs of odd functions? Odd functions are symmetric about the origin

22. EVEN

23. ODD

24. Neither

25. Neither

26. EVEN

27. ODD

28. Neither

29. EVEN