2.1 relations and functions
- 1. 2-1: Functions & Their Graphs Objectives: • I will determine if a relation is a function. • I will determine domain and range of a relation from a graph, from a table, or from an equation with and without restrictions.
- 2. Relations & Functions Relation: a set of ordered pairs Domain: the set of x-coordinates Range: the set of y-coordinates When writing the domain and range, do not repeat values.
- 3. Relations and Functions Given the relation: {(2, -6), (1, 4), (2, 4), (0,0), (1, -6), (3, 0)} State the domain: D: {0,1, 2, 3} State the range: R: {-6, 0, 4}
- 4. Relations and Functions • Relations can be written in several ways: ordered pairs, table, graph, or mapping. • We have already seen relations represented as ordered pairs.
- 5. Table {(3, 4), (7, 2), (0, -1), x y (-2, 2), (-5, 0), (3, 3)} 3 4 7 2 0 -1 -2 2 -5 0 3 3
- 6. Mapping • Create two ovals with the domain on the left and the range on the right. • Elements are not repeated. • Connect elements of the domain with the corresponding elements in the range by drawing an arrow.
- 7. Mapping {(2, -6), (1, 4), (2, 4), (0, 0), (1, -6), (3, 0)} 2 -6 1 4 0 0 3
- 8. Functions • A function is a relation in which the members of the domain (x-values) DO NOT repeat. • So, for every x-value there is only one y-value that corresponds to it. • y-values can be repeated.
- 9. Functions • Discrete functions consist of points that are not connected. • Continuous functions can be graphed with a line or smooth curve and contain an infinite number of points.
- 10. Do the ordered pairs represent a function? {(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)} No, 3 is repeated in the domain. {(4, 1), (5, 2), (8, 2), (9, 8)} Yes, no x-coordinate is repeated.