1. 3.1 Functions

2. X is called the independent variable Y is called the dependent variable

4. Operations on Functions

5. Domain on Operations

6. Perform each mathematical operation and state the domain on each operation.

8. A function is continuous over an interval of its domain if its hand-drawn graph over that interval can be sketched without lifting the pencil from the paper. Discontinuous at x = -2 Continuous Function

10. 5.1 Composite Functions

11. Composite Functions

12. Find each of the following. Composite Functions

13. Form the following composite functions and state the domain.

14. Composite Functions

15. Form the following composite functions and state the domain.

16. Find possible functions for f and g. Decomposition

17. 5.2 Inverse Functions

18. If (x, y) is on the graph of a relation, then (y, x) is on the graph of its inverse. Inverse Relations

20. One to One Functions A function is one-to-one if every x has exactly one y-value and every y has exactly one x-value

21. Other Relations

22. If every horizontal line intersects the graph of a function f in at most one point, then f is one–to–one. Not One–to– One One–to– One Horizontal Line Test

23. Inverse Functions

27. Finding the inverse of a domain- restricted function Inverse Functions

28. Finding the inverse of a domain- restricted function If the inverse is not one-to-one, restrict the domain to make the inverse correct. Inverse Functions