Objective SWBAT use graphs to represent relations and functions

Section 8.1 “Relations and Functions” Age (years), x 2 4 5 7 Length (in.), y 32 59 65 69 96 The relationship between age and length can be represented using ordered pairs. (2, 32), (4, 59), (5, 65), (5, 69), (7, 96) The ordered pairs form a RELATION. RELATION a pairing of numbers from one set, called the DOMAIN, with the numbers in another set, called the RANGE.

RELATION- DOMAIN contains numbers called INPUTS Consists of the following: DOMAIN contains numbers called INPUTS RANGE contains numbers called OUTPUTS The INPUTS are the X-coordinates and the OUTPUTS are the Y-coordinates.

RELATION Set 1 Set 2 Domain Range Input Output X-coordinate a pairing of numbers from one set, called the DOMAIN, with the numbers in another set, called the RANGE. Set 1 Set 2 Domain Range Input Output X-coordinate Y-coordinate

RELATION x 2 4 6 8 y 1 3 In addition to using ordered pairs or a table to represent a relation, you can also use a GRAPH or a MAPPING DIAGRAM. MAPPING DIAGRAM GRAPH Input Output 2 4 6 8 1 2 3 4

Represent the relation as a graph and mapping diagram. (1,10), (2, 15), (3, 10), (3, 20), (4, 25) MAPPING DIAGRAM GRAPH Input Output 1 2 3 4 10 15 20 25

The domain is the set of inputs: 10, 12, 13, Identify the domain and range of a relation The input-output table shows the cost of various amounts of regular unleaded gas from the same pump. Identify the domain and range of the relation. 10 Input gallons Output dollars 12 13 17 19.99 23.99 25.99 33.98 19.99, 23.99, 25.99, and 33.98. The domain is the set of inputs: 10, 12, 13, and 17.The range is the set of outputs:

Each input must be paired with only ONE output FUNCTION- Is a relation in which for each input there is EXACTLY ONE output. FUNCTION NOT A FUNCTION 2 4 6 8 0 1 0 1 3 5 5 1 2 3 Each input must be paired with only ONE output

FUNCTION- Is a relation in which for each input there is EXACTLY ONE output. FUNCTION NOT A FUNCTION When a relation is represented as a graph, you can use the VERTICAL LINE TEST. If you can draw a vertical line through any two points on the graph, then the relation is NOT a function.

“To Be or Not To Be” a FUNCTION 1 2 Output 12 9 6 3 Input 3 2 1 Output 7 4 Input FUNCTION NOT A FUNCTION 3 6 9 12 1 2 2 1 2 4 7 0 1 2 3 The pairing is a function because each input is paired with exactly one output. The pairing is not a function because each input is not paired with exactly one output.

DO NOW Pg. 387 Guided Practice Problems 1-7

Homework Text p. 388, #8-22 evens and #19