1. 3.1 Functions x is called the independent variable
y is called the dependent variable

3. Domain on Operations

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

5. 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

7. 5.1 Composite Functions

8. Composite Functions

9. Find each of the following
Composite Functions
Find each of the following

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

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

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

13. Find possible functions for f and g
Decomposition
Find possible functions for f and g

14. 5.2 Inverse Functions

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

16. Inverse Relations

17. 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
One to One Function

18. Not a One to One Function
Other Relations
Not a One to One Function
Not aFunction

19. Horizontal Line Test
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

20. Inverse Functions

21. Inverse Functions

22. Show that the functions are inverses of each other
Inverse Functions
Show that the functions are inverses of each other