Lesson 8.1 Relations and Functions Essential Question: How do you represent relations and functions?

Before we start… Label the coordinate plane: x-axis y-axis Origin Quadrants I - IV

Before we start… ITunes is having a major sale on music right now. Songs cost $0.50 each! What is your cost if you buy… 4 songs? 8 songs? 12 songs? 20 songs? Do you notice a pattern?

What is a relation? A set of ordered pairs Relates an input and an output

What is an… input? the x values output? the y values

What are… Domain? Range? Set of all possible input values (x) Set of all possible output values (y)

The table below shows the ages and lengths of five alligators The table below shows the ages and lengths of five alligators. Identify the domain and range of the relation. Age (years), x 2 4 5 7 Length (inches), y 32 59 65 69 96

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 function. Input (gallons) 10 12 13 17 Output (dollars) 19.99 23.99 25.99 33.98

Identify the domain and range of the function. Input 1 2 4 Output 5

Identify the domain and range Input Output 5 1 7 2 15 3 44

Identify domain and range

Identify domain and range Input Output 6 5 12 7 21 10 42 17

How do you represent relations and functions? Ordered pairs Tables Graphs Mapping diagrams

Mapping Diagrams A function may be represented by a mapping diagram. An output may be paired with more than one input, but no input is paired with more than one output.

Represent the relation −1,1 , 2,0 , 3,1 , 3,2 , 4,5 as indicated. a Represent the relation −1,1 , 2,0 , 3,1 , 3,2 , 4,5 as indicated. a. A graph b. A mapping diagram

Represent the relation 0,3 , 1,2 , 2,−1 , 4,4 , 5,4 as indicated. a Represent the relation 0,3 , 1,2 , 2,−1 , 4,4 , 5,4 as indicated. a. A graph b. A mapping diagram

What is a function? A special relation Each input has exactly one output Each x has one y

How does a function work? A function rule assigns each number in the domain to exactly one number in the range.

Ways to Look at a Function Verbal Rule The output is 3 more than the input. Equation y = x + 3 Table

How do I identify a function? Each input will have only ONE output. Tables and ordered pairs can be used to identify a function.

Tell whether the pairing is a function

Tell whether the relation is a function. Input 9 25 Output 3 -3 5 -5 Input -4 4 8 Output 32

Tell whether the relation is a function. Input 3 6 9 12 Output 1 2 Input 2 4 7 Output 1 3

Tell whether the relation is a function. 0,2 , 1,4 , 2,6 , 3,8 −2,4 , 2,4 , 4,2 , −2,−4

Tell whether the relation is a function. 3,−2 , 6,1 , −3,5 , 4,1 5,1 , 5,3 , 7,1 , 8,4

Vertical Line Test You can use the graph of a relation to determine whether it is a function.

Are these functions?

Is this a function?

Is this a function?

Tell whether the relation is a function Tell whether the relation is a function. If it is, is the function linear?

Tell whether the relation is a function Tell whether the relation is a function. If it is, is the function linear?

Tell whether the relation is a function Tell whether the relation is a function. If it is, is the function linear?

How do you represent relations and functions?

Ticket Out the Door Identify the domain and range of the relation. 0,0 , 1,2 , 2,4 , 3,6 , 4,8