Objectives: Identify functions. Find the domain and range.

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}

1. 2. x y Give the domain and range of the relation. 1 4 8 1. 2. 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?

3. 4. x y Give the domain and range of the relation. 3 -4 7 -1 20 12 3. 4. 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. 6. Give the domain and range of the relation. Domain: -4 to 5 5. 6. Domain: -4 to 5 Domain: All real numbers Range: 1 Range: All real numbers

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

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

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

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

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

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.

“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!!!

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

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.

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!!!

10. 11. Give the domain and range of the relation. Tell whether the relation is a function. Explain. 10. 11. {(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.

12. 13. Give the domain and range of the relation. Tell whether the relation is a function. Explain. 12. 13. 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.