Section 4.1

Properties of functions

You are expected to take notes in a

bound notebook.

Chapter 4 test will be on

Wed Oct 8, 2014

A blast from the past:

Symbols:

Graphs of single variable inequalities:

Click here to see examples of each.

What does the

infinity symbol in a

math class mean?

Deep and Wide:

Domain & Range

The student is expected to identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete

A function is a set of ordered pairs of

numbers (x, y) such that no x –values

are repeated.

What are the domain and range of a

function?

The domain and range of a function are

sets that describe those ordered pairs.

Definition Example

{(3, 6), (2, 8), (5,

3)}

Domain All the x-coordinates in

the function's ordered

pairs

{ 3, 2, 5}

Range All the y-coordinates in

the function's ordered

pairs

{ 6, 8, 3}

The domain is the set of all the values of the independent variable, the x-coordinate

The range is the set of all the values of the dependent variable, the y-coordinate.

Identify the domain and range of the

function below.

{ 2, 7), (4, 11), (6, 15), (8, 19)}

The domain is { 2, 4, 6, 8}

The range is { 7, 11, 15, 19}

Graphs

The domain of a function is the set of all the

x-coordinates in the functions’ graph

Domain 3 ≤ x ≤ 12

The range of a function is the set of all the y-

coordinates in the functions’ graph

Range 6 ≤ y ≤ 12

What is the domain of this function?

What is the range of this function?

Domain is 0 ≤ x ≤ 4

Range is 1 ≤ y ≤ 5

The graph shows the path of a golf ball

Which of following

describes the range

of this function?

a) 0 < y < 100

b) 0 ≤ y ≤ 100

c) 0 ≤ x ≤ 5

d) 0 < x < 5

What is the domain of this function?

A -1 ≤ x ≤ 5

B -1 ≤ x ≤ 9

C 2 ≤ x ≤ 5

D 0 ≤ y ≤ 9

What is the domain of the function

shown on the graph?

A -2 < y ≤ 2

B -4 ≤ x ≤ 6

C -4 < y ≤ 2

D -2 < x ≤ 6

Sometimes you will be asked to

determine a REASONABLE domain

or range

The average daily high temperature for the

month of May is represented by the function

t = 0.2n + 80

Where n is the date of the month. May has 31

days. What is a reasonable estimate of the

domain?

Answer: 1 ≤ n ≤ 31

What is a reasonable estimate of the range

Answer: See next slide

Our function rule is:

t = 0.2n + 80

Our domain is 1 ≤ n ≤ 31

Our smallest possible n is 1

Our largest possible n is 31

To find the range, substitute 1 into the equation

and solve. Then substitute 31 into the

equation and solve.

Our function rule is:

t = 0.2n + 80

Substitute a 1

t = 0.2n + 80

t = 0.2(1) + 80

t = 0.2 + 80

t = 80.2

Substitute a 31

t = 0.2n + 80

t = 0.2(31) + 80

t = 6.2 + 80

t = 86.2

Reasonable range is 80.2 ≤ t ≤ 86.2

State the domain and range of the

following function:

-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9

-9-8

-7

-6-5

-4

-3-2

-1

1

23

4

56

7

89

x

y

State the domain and range of the

following function:

The Vertical Line Test

The vertical line test is used to

determine if a graph is a function.

If a vertical line passes through a graph more than once,

the graph is not the graph of a function.

Hint:

Pass a pencil across

the graph held

vertically to represent

a vertical line.

The pencil crosses the graph

more than once. This is not a

function because there are

two y-values for the same x-

value.

Homework expectation:

All homework is due the next class period.

Grace period of one week is provided but you

are responsible to keep track of the deadlines…

there will be no reminders.

On your own:

Read section 4.1.

Make sure your

classroom notes are

complete and

pretty!

Give a complete solution

to the following

problems:

Section 4.1 page 122

Written exercises #1-11

odds and then 13-18 all.