UNDERSTANDING RELATIONS AND FUNCTIONS...

ALGEBRA

1. RELATIONS a set of ordered pairs

2. A relation can be represented by a set of ordered pairs, a table, a graph, or a mapping .

3. The DOMAIN (input) of a relation is the x-coordinates of the ordered pairs. The RANGE (output) of a relation is the y-coordinates of the ordered pairs.

4. The INVERSE of a relation is found by switching the coordinates of each ordered pair.

5. FUNCTIONS a relation when each element of the domain is paired with exactly one element of the range. For every x there is exactly one y . The x-coordinate cannot repeat.

6. EXAMPLES THAT ARE FUNCTIONS: EXAMPLES THAT ARE NOT FUNCTIONS:

7. VERTICAL LINE TEST test used to decide if a graph is a function.

8. EXAMPLE: FUNCTION! If no vertical line can be drawn so that it intersects the graph more than once, then the graph IS a function.

9. EXAMPLE: NOT A FUNCTION! If any vertical line can be drawn so that it intersects the graph at two or more points, then the relation IS NOT a function.

10. FUNCTION NOTATION the y is replaced with f(x), read “f of x”

11. EVALUATING FUNCTIONS:

12. ANOTHER EXAMPLE:

13. THANK YOU!