1. DOMAIN AND RANGE Section 16.2

2. Functions Identify relations, domains, and ranges.

3. Identifying Relations, Domains, and Ranges A set of ordered pairs is called a relation.  Could be a list of ordered pairs, a table of values, a graph, or an equation The set of permissible x-values of the relation is the domain.  The input of a relation. The set of permissible y-values of the relation is the range.  The output of a relation.

4. Identifying Relations, Domains, and Ranges Find the domain and range of the relation. 1. {(-3, 5), (-3, 1), (4, 6), (7, 0)} 2. 3. 4. x25712 y42549144 Year Billions of Dollars 200616.7 200720.3 200823.5 200926.6 201029.4 Domain: {-3, 4, 7} Domain: {2006, 2007, 2008, 2009, 2010} Domain: {2, 5, 7, 12} Domain: {-2, 0, 1, 3} Range: {5, 1, 6, 0} Range: {4, 25, 49, 144} Range: {16.7, 20.3, 23.5, 26.6, 29.4} Range: {-3, 1, 2}

5. Identifying Relations, Domains, and Ranges The previous represented discrete data.  Individual points that would not be connected when graphed because not all rational values define the domain. When the data is continuous, you must represent the domain and range using interval notation.  Interval must be written smallest to biggest.  [ and ] used when the end point is included in the interval.  ( and ) used when the end point is not included in the interval or with -∞ and ∞.

6. Identifying Relations, Domains, and Ranges Find the domain of the relation. Find the range of the relation.

7. Identifying Relations, Domains, and Ranges Find the domain of the relation. Find the range of the relation.

8. Identifying Relations, Domains, and Ranges Find the domain of the relation. Find the range of the relation. “hole”