1. Determining the Key Features of Function Graphs 10 February 2011

2. The Key Features of Function Graphs - Preview  Domain  Range  x-intercepts  y-intercept  End Behavior  Intervals of increasing, decreasing, and constant behavior  Parent Equation  Maxima and Minima

3. Domain  Reminder: Domain is the set of all possible input or x-values  When we find the domain of the graph we look at the x-axis of the graph

4. Determining Domain - Symbols  Open Circle →  Exclusive  ( )  Closed Circle →  Inclusive  [ ]

5. Determining Domain 1. Start at the origin 2. Move along the x-axis until you find the lowest possible x-value. This is your lower bound. 3. Return to the origin 4. Move along the x-axis until you find your highest possible x-value. This is your upper bound.

6. Examples Domain:

7. Example Domain:

8. Determining Domain - Infinity Domain:

9. Examples Domain:

10. Your Turn:  In the purple Precalculus textbooks, complete problems 3, 7, and find the domain of 9 and 10 on pg. 160 3.7. 9.10.

11. Range  The set of all possible output or y- values  When we find the range of the graph we look at the y-axis of the graph  We also use open and closed circles for the range

12. Determining Range  Start at the origin  Move along the y-axis until you find the lowest possible y-value. This is your lower bound.  Return to the origin  Move along the y-axis until you find your highest possible y-value. This is your upper bound.

13. Examples Range:

14. Examples Range:

15. Your Turn:  In the purple Precalculus textbooks, complete problems 4, 8, and find the domain of 9 and 10 on pg. 160 4.8. 9.10.

16. X-Intercepts  Where the graph crosses the x-axis  Has many names: x-intercept Roots Zeros

17. Examples x-intercepts:

18. Y-Intercepts  Where the graph crosses the y-axis y-intercepts:

19. Seek and Solve!!!