1. 1.5 I understand Functions

2. Function For each input there is only one output Ex: Let g represent the age of a US citizen and d represent the number of days since his or her birth. Is g a function of d or is d a function of g?

3. If y is a function of x

4. Relation A set of ordered pairs Can be indicated by a verbal description, a graph, a formula or equation, or a table Not every relation is a function, but every function is a relation.

5. Determine if each relation is a function: XY 19 2029 610 9 XY 57 68 79 56

6. Vertical Line Test A graph is a function if and only if there is no vertical line that crosses the graph more than once AKA: When you draw a vertical line on the graph, if it intersects with the graph more than once, it is NOT a function

7. Use the Vertical Line Test to determine if the graph is a function

8. Identifying a function from an equation

9. Domain and Range

10. Determine the Domain and Range (Put into calculators if needed)

11. Function Notation

12. Using Function Notation

13. Using Function Notation with Variables

14. The Average Rate of Change Slope = It is not necessary to have a formula for a function to find the average rate of change, you can find the average rate of change (slope) if you know two points on the graph.

15. Average Rate of Change (slope) Find the average rate of change between the two points.

16. Example 1 The population of California was 29.8 million in 1990 and 33.9 million in 2000. What was the average rate of change of the population over that time interval? Use the coordiantes (year, population) (1990, 29,800,000) and (2000, 33,900,000)

17. The Difference Quotient

18. Find and simplify the difference quotient

19. Find and simplify the difference quotient

20. Find and simplify the difference quotient

21. 1.6 Graphs of Relations and Functions Parent Functions Graph the following parent functions and state the domain and range.

22. XY

23. XY

24. XY The Absolute Value Function

25. The square root function: XY

26. The Cubic function: XY

27. XY

28. XY

29. XY

30. XY