1. Relations and Functions

2. A relation is _____________________________
________________________________________.

3. There are four ways to represent a relation: ORDERED PAIRS
{(1, 5), (2, 3), (3, 2), (4, 1)}
TABLE OF VALUES GRAPH MAPPING DIAGRAM ç

4. Examples
1. Express the relation {(1, 3), (2, 4), (3, 5)} as a table, graph, and mapping diagram. ç

5. Examples
2. Express the relation as a set of ordered pairs, a graph, and mapping diagram. ç

6. The domain of a relation is _____________________
____________________________________________.
The range of a relation is _______________________

7. Examples
Determine the domain and range for each relation.
D: ________ D: _________ D: _________
R: ________ R: _________ R: _________

8. The function is _______________________________
____________________________________________.
Examples
Determine the domain and range for each relation. Then determine whether the relation is a function.
6. {(3, -2), (5, -1), (4, 0), (3, 1)}
D: ____________________  
R: ____________________ 
Function? _____________

9. Examples
Determine the domain and range for each relation. Then determine whether the relation is a function.
D: ___________ D: _____________  
R: ___________ R: _____________  
Function? _____ Function? _______

10. The vertical line test is _______________________
____________________________________________.
Examples
Use the vertical line test to determine whether the graph shows a function.

11. Putting It All Together
Determine the domain and range for each relation. Then determine whether the relation is a function.
D: ________ D: ________ D: ________  
R: ________ R: ________   R: ________
Function? __ Function? __ Function? __

12. Graphing Functions

13. 1) Graph the function for the given domain: x – 3y = -6; D: {-3, 0, 3, 6}
Step 1: ________________________________________________________
Step 2: ________________________________
Step 3: ___________________________________ x y

14. 2) Graph the function for the given domain: f(x) = x2 - 3; D: {-2, -1, 0, 1, 2} **Reminder**___________________________________________________ x y

15. 3) Graph the function for the given domain: f(x) =|x|; D: {-2, -1, 0, 1, 2}y

16. 4) Graph the function for the given domain: -2x + y = 3; D: {-5, -3, 1, 4}

17. 5) Graph the function for the given domain: f(x) = x2 + 2; D: {-3, -1, 0, 1, 3}y

18. We are not always given a specific set of domain values
We are not always given a specific set of domain values. When that is the case, we assume that the domain is _________________________________. In other words, __________________________________________________ _______________________________________________________________ 6) Graph the function -x + 2y = 6 x y

19. Graph the function g(x) =|x|+ 2y

20. 8) Graph the function y = x2

21. Finding Values Using Graphs
Use the graph of the function f(x) = x + 4 to find the value of f(x)
when x = -4
Check:

22. Finding Values Using Graphs
10) Use the graph of the function f(x) = x + 2 to find the value of f(x)
when x = 3
Check:

23. Word Problem: A mouse can run 3. 5 meters per second
Word Problem: A mouse can run 3.5 meters per second. The function y = 3.5x describes the distance in meters the mouse can run in x seconds. Graph the function then use the graph to estimate how many meters a mouse can run in 2.5 seconds. x y