math math in life and applicationFUNCTIONS.ppt

math

1. FUNCTIONS
CONTENTS:
• Functions and Their Graphs.
• Combining Functions; Shifting and Scaling Graphs.

2. Functions and Their Graphs
When the range of a function is a set of real numbers, the
function is said to be real-valued.
The domains and ranges of many real-valued functions of a real
variable are intervals
or combinations of intervals. The intervals may be open, closed,
or half open, and may
be finite or infinite. The range of a function is not always easy to
find.

3. Functions and Their Graphs

4. Functions and Their Graphs

5. Functions and Their Graphs

6. Functions and Their Graphs

7. Functions and Their Graphs

8. Functions and Their Graphs

9. Functions and Their Graphs

10. Functions and Their Graphs

11. Functions and Their Graphs

12. Functions and Their Graphs

13. Functions and Their Graphs

14. Functions and Their Graphs

15. Functions and Their Graphs

16. Functions and Their Graphs

17. Functions and Their Graphs

18. Combining Functions; Shifting and Scaling
Graphs

19. Combining Functions; Shifting and Scaling
Graphs

20. Combining Functions; Shifting and Scaling
Graphs

21. Combining Functions; Shifting and Scaling
Graphs

22. Exercises

23. Trigonometric Functions

24. Trigonometric Functions

25. Trigonometric Functions

26. Exercises

27. Exercises

28. Exercises