Transcript Deep and Wide: Domain & Range

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:
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Symbols:
Graphs of single variable inequalities:
Click here to see examples of each.
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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.
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What are the domain and range of a
function?
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The domain and range of a function are
sets that describe those ordered pairs.
Definition
Domain All the x-coordinates in
the function's ordered
pairs
Range
All the y-coordinates in
the function's ordered
pairs
Example
{(3, 6), (2, 8), (5,
3)}
{ 3, 2, 5}
{ 6, 8, 3}
The domain is the set of all the values of
the independent variable, the xcoordinate
The range is the set of all the values of
the dependent variable, the ycoordinate.
Identify the domain and range of the
function below.
{ 2, 7), (4, 11), (6, 15), (8, 19)}
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The domain is { 2, 4, 6, 8}
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The range is { 7, 11, 15, 19}
Graphs
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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 ycoordinates 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
-9 -8 -7 -6 -5 -4 -3 -2 -1 -1
-2
-3
-4
-5
-6
-7
-8
-9
y
x
1
2
3
4
5
6
7
8
9
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 xvalue.
Homework expectation:
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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!
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Give a complete solution
to the following
problems:
Section 4.1 page 122
Written exercises #1-11
odds and then 13-18 all.