3.5 Domain of a Rational Function Thurs Oct 2 Do Now Find the domain of each function 1) 2)
Section 4.1 Properties of functionsA function is a set of ordered pairs of numbers (x, y) such that...
Transcript of Section 4.1 Properties of functionsA function is a set of ordered pairs of numbers (x, y) such that...
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Section 4.1
Properties of functions
You are expected to take notes in a
bound notebook.
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Chapter 4 test will be on
Wed Oct 8, 2014
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A blast from the past:
Symbols:
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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?
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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
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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.
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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}
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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.
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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}
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Graphs
The domain of a function is the set of all the
x-coordinates in the functions’ graph
Domain 3 ≤ x ≤ 12
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The range of a function is the set of all the y-
coordinates in the functions’ graph
Range 6 ≤ y ≤ 12
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What is the domain of this function?
What is the range of this function?
Domain is 0 ≤ x ≤ 4
Range is 1 ≤ y ≤ 5
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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
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What is the domain of this function?
A -1 ≤ x ≤ 5
B -1 ≤ x ≤ 9
C 2 ≤ x ≤ 5
D 0 ≤ y ≤ 9
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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
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Sometimes you will be asked to
determine a REASONABLE domain
or range
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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
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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.
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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
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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
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State the domain and range of the
following function:
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The Vertical Line Test
The vertical line test is used to
determine if a graph is a function.
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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.
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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.
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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.