1. Objectives:
Identify functions.
Find the domain and range.

2. Vocabulary Relation: Set of ordered pairs
Example: {(2,3),(-4,7),(0,2),(-4,5)}
Domain: The set of x-coordinates
{-4, 0, 2}
Range: The set of y-coordinates
{2, 3, 5, 7}

3. 1. 2. x y Give the domain and range of the relation. 1 4 8
x y 1 4 8
Domain: {1, 4, 8}
Domain: 1 to 5
Range: {1, 4}
Range: 3 to 4
Why do we write the domain
& range differently when
there is a graph?

4. 3. 4. x y Give the domain and range of the relation. 3 -4 7 -1 20 12
x y 3 -4 7 -1 20 12
Domain: {3, 7, 20}
Range: {-4, -1, 12}
Domain: -4 to 4
Range: -2 to 4

5. 5. 6. Give the domain and range of the relation. Domain: -4 to 5
Domain: -4 to 5
Domain: All real numbers
Range: 1
Range: All real numbers

6. A relation can be modeled 4 different ways:
Ordered pair {(x, y), (x, y), (x, y)}
Table
3. Graphing
4. Mapping (This is a new concept we will learn today.) x y

7. Mapping x y Draw two ovals. Label them x and y.
List the x and y values from smallest to biggest.
Draw an arrow connecting the points that correspond to one another.
x y

8. x y x y 7. 8. Map the following relations.
{(-2, 3) , (5, 7), (5, 6), (-1, 3)}
{(1, 3) , (4, -1), (5, 6), (-1, -8)}
x y
x y

9. x y x y Express the relation: {(1, 3), (2, 4), (3, 5)}
as a table, as a graph, and as a mapping diagram.
x y
x y

10. A function is a special type of relation that pairs each domain value (x) with exactly one range value (y).

11. To determine if a relation is or is not a function:
If any of the x values repeat, it is not a function (tables, ordered pairs).
2) If any x-value maps over (points) to more than one y-value, it is not a function.
3) If the graph of the relation fails the VERTICAL LINE TEST , it is not a function.

12. “4” appears twice in the x-values.
If any of the x values repeat, it is not a function. x y -2 1 4 7 6 3
“4” appears twice in the x-values.
THIS IS NOT A FUNCTION!!!

13. x y “5” maps (points) to -1 & 2. THIS IS NOT A FUNCTION!!!
2) If any x-value maps over to more than one y-value, it is not a function.
x y -1 2 8 7
“5” maps (points) to -1 & 2.
THIS IS NOT A FUNCTION!!! -2 5 6

14. Vertical Line Test If you draw a vertical line ANYWHERE on the graph…
If your graph touches the vertical line MORE THAN ONCE it is not a function.
If it only touches ONCE it is a function.

15. This graph does not pass the vertical line test!!
3) If the graph of the relation fails the VERTICAL LINE TEST , it is not a function.
This graph does not pass the vertical line test!!
THIS IS NOT A FUNCTION!!!

16. 10. 11. Give the domain and range of the relation.
Tell whether the relation is a function. Explain.
{(3, –2), (5, –1), (4, 0), (3, 1)}
D: {3, 5, 4}
R: {–2, –1, 0, 1}
D: {–4, –8, 4, 5}
The relation is not a function.
The domain value 3 is paired with the range values –2 and 1.
R: {2, 1}
This relation is a function.
Each domain value is paired with exactly one range value.

17. 12. 13. Give the domain and range of the relation.
Tell whether the relation is a function. Explain.
D: {2, 3, 4}
R: {–5, –4, –3}
D: –5 to 3 R: –2 to 1
The relation is not a function. The domain value 2 is paired with both –5 and –4.
The relation is not a function.
Does not pass VLT.