Relations and Functions Section 8.1 Relations and Functions pages 400 - 404

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)}

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:

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.

Identifying a Function

Identifying a Function

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

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)}

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.

Using the Vertical – Line Test

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

x y - 3 5 - 5 3

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

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