The document discusses how to classify relations and functions based on their sets of ordered pairs and graphs. A relation is classified as a function if each element of its domain corresponds to exactly one element of its range. A graph is a function if it passes the vertical line test, where no vertical line intersects the graph in more than one point. The document also defines domain as the set of possible input values and range as the set of possible output values for a relation or function. It provides examples of different domains and ranges.

1. Function or Not Function
SUBTITLE

2. The following summarizes how to classify correspondences as
relation only or functions.
Relation only Function

3. Set of Ordered Pair
Relation Only Function
1. A = { (1, 4), (1, 8), (1, 9), (1, 13)}
2. B = {(3, 9), (1, 0), (5, -2), (3, -1)}
3. C = {(2, 7), (-5, 0), (4, -2), (-5, -1)}
• Domain is paired with more than one
element
4. D = {(4, 9), (1, 7), (-5, -2), (5, -1)}
5. E = {(4, 9), (6, 9), (5, 9), (3, 9)}
6. B = {(3, -1), (1, 6), (5, 3), (0, -1)}

4. To determine whether a graph is a function or not, use a
vertical line test.

5. Graphs
Relation Only Function

6. Domain and Range
Domain refers to the set of possible input values, the domain of
a graph consists of all the input values shown on the x-axis. The range is
the set of possible output values, which are shown on the y-axis.

8. Example 3. Domain : all real numbers
Range: all real numbers
Example 4. Domain: x ≥ 0
Range: all real numbers

9. Example 4. Domain: x ≥ 0
Range: y ≥ 0
Example 5. Domain: all real numbers except x = 2
Range: all real numbers except y = 0

10. Example 5. Domain: -3 ≥ x < 3
Range: -4 ≤ y ≤ -2
Example 6. Domain: 1 ≥ x > -3
Range: -4 ≤ y < -3