SECT. 1.1 – DAY 2

WARM UPWrite the following in interval notation:

1) 2<x<5

2) 0<x≤14

Find the distance of the following:

3) and (, 6)

4) (7,-2) and (5,8)

OBJECTIVES

*Identify functions and use function notation.

*Find domain and range of functions.

RELATIONS

A relation is defined as a set of ordered pairs. Many relations have a rule or formula showing the connection between the two components of the ordered pairs.

*Most relations we use in trigonometry are functions.

THINKING ABOUT FUNCTIONS…

The input in the diagram to the right refers to the __ values of the function.

The output in the diagram to the right refers to the __ values of the function.

Let’s take a look at the function:

y = -3x + 5

FUNCTIONSA relation is a function if each value of the independent variable leads to exactly one value of the dependent variable.

We can write functions as:

y = -3x + 5

Or

f(x) = -3x + 5

We say f(x) as “f of x”

ARE THESE RELATIONS FUNCTIONS? WHY OR WHY NOT?

USING FUNCTION NOTATION

Let f(x) = -3x2 + 2x – 4

Find:

1) f(0)

2) f(-3)

3) f(2)

VERTICAL LINE TEST

If every vertical line intersects the graph of the function in no more than one point, then the graph is a graph of a function.

FINDING DOMAIN AND RANGE OF RELATIONS Domain refers to all of the ______ values in a relation.

Range refers to all of the ______ values in a relation.

EXAMPLE

Find the domain and range of the relation. Is it a function?

EXAMPLE

Find the domain and range of the relation. Is this a function?

EXAMPLE

Find the domain and range of the relation. Is this a function?

GROUP ACTIVITYEach group is to come up with five relations on a piece of paper.

There must be at least one relation that is not a function.

There must be two relations drawn as a graph, two relations written in function notation, and one of your choice.

You should have two sheets: one sheet with just the problems on there and one sheet with the answer key.

The answer key should express whether the relation is a function as well as finding the relations’ domain and range!

INDEPENDENT WORK

Work on the back of the worksheet that was last night’s homework.

HOMEWORK

Domain & Range Worksheet #1-8