1. Relations and Functions
Section 8.1
Relations and Functions
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2. The data in the table could be written as a relation.
A relation is a set of ordered pairs.
Here is the relation represented by the table:
{(25,133),(22,216),(24,148),(22,195),(20,74),(21,150)}

3. The first coordinates are the domain of the relation.
{(25,133),(22,216),(24,148),(22,195),(20,74),(21,150)}
The braces, { }, indicate that these are all the ordered pairs in this relation.
The first coordinates are the domain of the relation.
The second coordinates are the range of the relation.
DOMAIN:
RANGE:

4. Some relations are functions.
In a function, each member of the domain is paired with exactly one member of the range.
You can draw a mapping diagram to see whether a relation is a function.

5. Identifying a Function

6. Identifying a Function

7. {(0,5), (1,6), (2,4), (3,7)} Domain:{ } Range: { } Function?
Example:
{(0,5), (1,6), (2,4), (3,7)} Domain:{ } Range: { } Function?

8. Identifying a Function
Is each relation a function? Explain. A) {(0, 5), (1, 5), (2, 6), (3, 7)} B) {(0, 5), (0, 6), (1, 6), (2, 7)}

9. Graphing Relations & Functions
Graphing a relation on a coordinate plane gives us a visual way to tell if a relation is a function. If the relation is a function, then any vertical line passes through at most one point on the graph. If a line passes through two points on the graph, then the relation is not a function. This is the vertical-line test.

10. Using the Vertical – Line Test

11. The pencil held vertically would pass through both (2,0) and (2,3), so the relation is not a function.

12. x y
- 3 5
- 5 3

13. x y
- 6
- 5
- 3
- 2 1 4 3 5 7

14. x y
- 7 4
- 2 6
- 1 3 5 1