Relations and Functions

A relation is _____________________________ ________________________________________.

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

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

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

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

Examples Determine the domain and range for each relation. 3. 4. 5. D: ________ D: _________ D: _________   R: ________ R: _________ R: _________

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? _____________

Examples Determine the domain and range for each relation. Then determine whether the relation is a function. 7. 8. D: ___________ D: _____________   R: ___________ R: _____________   Function? _____ Function? _______

The vertical line test is _______________________ ____________________________________________. Examples Use the vertical line test to determine whether the graph shows a function. 9. 10. 11.  

Putting It All Together Determine the domain and range for each relation. Then determine whether the relation is a function. 12. 13. 14. D: ________ D: ________ D: ________   R: ________ R: ________   R: ________ Function? __ Function? __ Function? __

Graphing Functions

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

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

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

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

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

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

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

8) Graph the function y = x2

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:

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:

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