Functions: Intervals of Increasing and Decreasing

1. Functions: Intervals of Increasing and Decreasing By: Mr. Burton Rockvale High School Materials: Calculator, Paper, Pencil, Notes (Computer in your desk)

2. Learning intentions: • Identify Maximums and Minimums using Graphing Calculator • Identify increasing, decreasing, constant intervals • Determine End Behaviors (Review)

3. The x intercept is where the graph crosses the x axis. x and y intercepts • The y intercept is where the graph crosses the y axis. x intercepts

4. The x intercept is a point in the equation where the y-value is zero. x and y intercepts Example: Find the x intercepts of Set y =0, solve for x. x intercepts:

5. x and y intercepts The y intercept is a point in the equation where the x-value is zero. Example: Find the y intercepts of Set x =0, solve for y. y intercepts: (0,-2) (0,2)

6. Increasing, Decreasing,Constant Intervals A function f is increasing on an interval if as x increases, then f(x) increases. A function f is decreasing on an interval if as x increases, then f(x) decreases. A function f is constant on an interval if as xincreases, then f(x) remains the same.

7. Increasing, Decreasing, Constant Intervals A function f is increasing on an interval if as x increases, then f(x) increases. A function f is decreasing on an interval if as x increases, then f(x) decreases. f(x) is decreasing in the interval . f(x) is increasing in the interval . vertex (1.5,-2)

8. Answer Now Increasing, Decreasing, Constant Intervals A function f is increasing on an interval if as x increases, then f(x) increases. A function f is decreasing on an interval if as x increases, then f(x) decreases. A function f is constant on an interval if as xincreases, then f(x) remains the same. Find the interval(s) over which the interval is increasing, decreasing and constant?

9. Increasing, Decreasing, Constant Intervals A function f is increasing on an interval if as x increases, then f(x) increases. A function f is decreasing on an interval if as x increases, then f(x) decreases. A function f is constant on an interval if as xincreases, then f(x) remains the same. f(x) is decreasing in the interval (-1,1). f(x) is increasing in the intervals

10. Answer Now Increasing, Decreasing, Constant Intervals A function f is increasing on an interval if as x increases, then f(x) increases. A function f is decreasing on an interval if as x increases, then f(x) decreases. A function f is constant on an interval if as xincreases, then f(x) remains the same. Find the interval(s) over which the interval is increasing, decreasing and constant?

11. Increasing, Decreasing, Constant Intervals A function f is increasing on an interval if as x increases, then f(x) increases. A function f is decreasing on an interval if as x increases, then f(x) decreases. A function f is constant on an interval if as xincreases, then f(x) remains the same. f(x) is decreasing over the intervals f(x) is increasing over the interval (3,5). f(x) is constant over the interval (-1,3).

12. End Behavior of Functions The end behavior of a graph describes the far left and the far right portions of the graph. Using the leading coefficient and the degree of the polynomial, we can determine the end behaviors of the graph. This is often called the Leading Coefficient Test.

13. End Behavior of Functions First determine whether the degree of the polynomial is even or odd. degree = 2 so it is even Next determine whether the leading coefficient is positive or negative. Leading coefficient = 2 so it is positive

14. END BEHAVIOR Degree: Even Leading Coefficient: + End Behavior: UpUp

15. END BEHAVIOR Degree: Even Leading Coefficient: End Behavior: DownDown

16. END BEHAVIOR Degree: Odd Leading Coefficient: + End Behavior: Down Up

17. END BEHAVIOR Degree: Odd Leading Coefficient: End Behavior: UpDown

18. END BEHAVIOR PRACTICE Give the End Behavior:

19. END BEHAVIOR PRACTICE Give the End Behavior: Up Down Up Up Down Up Down Down

20. Student.desmos.com • Get out your computer • Log-in using your school ID • Go to student.desmos.com • Use Code • 2nd: GWRTSQ • 6th: VXDEEB