Transcript Interval Notation

Welcome Back!
Aug 11th
Algebra 2 with Mr. Xiong
Desk
Fold hotdog style
Center – Your first, Last
name (large in the
middle, on both sides)
Fill out who am I form.
Introduce yourself to some
sitting next to you.
Share :
Tell the class who the
other person is.
3 things about him/her
Algebra 2 course Expectations
Course Description: Algebra II is a college prep course and is a
requirement for acceptance to all CSU and UC schools. Many new
concepts and techniques will be introduced as preparation to future math
courses. The emphasis will be operating with variables, solving different
types of equations, and graphing various functions.
Daily Materials:
Bring the following to class with you every day:
 Textbook
 Line paper / Graph Paper
 Pencil/ Color Pens/pencil / highlighters / rulers
 3-ring binder / notebook
 Whiteboard marker ( dry erase marker)
 Graphing Calculator. TI–83, TI–84 or TI–89
Notebook
Classroom Rules:
Classroom Rules: Students are expected to follow the
guidelines/expectations outlined in the student handbook. In order
to create a safe and positive classroom environment, we expect
you to always:
BE SAFE:
Keep hands, feet, and objects to yourself
BE RESPONSIBLE:
Be on time in your seat when the bell rings
Be prepared to learn by bringing materials, and participate,
No gum or food, except water
Sharpen your pencils before the bell rings
Do not cheat
BE RESPECTFUL:
Be a good listener - Avoid interrupting when other people are
talking
Use appropriate language
Do not distract other students from learning
Follow directions
Do not leave your desk without asking permission, even to
throw away trash or sharpen your pencil
Working on other subjects is permitted only if you have
finished your math assignment
Class Room Procedures
• Enter the classroom
– Enter quietly, go to your seat. Take off
hat.
– Check homework - Find your mistakes,
Ask study team for help.
– Keep your voices down
• During Class
– Take notes in notebook
– Remove backpack/purse off disk.
– Listen / no talking
• Group Work
– Follow Study Team
Expectations
– Stay in your seat
• Leaving class
– Only pack up the last min
of class.
– Pick up any trash around
you
– Straighten up your seats
– Turn in your homework in
the turn-in basket.
Learning targets
Notebook
First Page
Table of content
1) 1-1 Sets of
Numbers /1.2
Properties of
Numbers
Page
1
Composition Book
(Notebook )
1
Table of content
1) 1-1 Sets of
Numbers /1.2
Properties of
Numbers
Skip about 3
page then start
your notes
Page
1
1) 1-1 Sets of Numbers /1.2 Properties of
Numbers
● Irrational: Cannot be written
as a fraction
● Whole Numbers: Positive
Whole numbers including 0
● Natural Numbers: “Counting”
numbers
● Integers: Positive and
negative whole numbers
● Rational: Anything that can
be written as a fraction
● Real Numbers:
Everything on the
number line.
Set: Collect or group of items ( Element)
A = (1, 2, 3)
Subset : A smaller set (group) who belongs to the larger
group
B = (1, 2, 3)
B = (1, 2)
B = (1)
B = (1, 3)
B = (2)
B = (2, 3)
B = (3)
Something to think about Question: B is a subset of A
what possible sets could represent B?
Step 1:
Put all numbers in decimal form
Step 2:
Put the numbers in order
You try! Order the numbers in roster
notation from least to greatest
Consider the numbers –2, , –0.321,
and
Step 1:
Put all numbers in decimal form
Step 2:
Put the numbers in order
,
.
Interval Notation
In interval notation the symbols [ and ] are used to include an
endpoint in an interval, and the symbols ( and ) are used to
exclude an endpoint from an interval.
Inequality
3<x<5
-2
-1
0
(3, 5)
1
2
3
4
5
6
7
8
interval notation
The set of real numbers between but not
including 3 and 5.
Interval Notation
Words
Number less
than 3
Numbers
greater than
or equal to -2
Numbers
between 2
and 4
Numbers 1
through 3
Number line
Inequality
Interval notation
Interval Notation solutions
You try!
Use interval notation to represent the set of
numbers.
7 < x ≤ 12
(7, 12]
7 is not included, but 12 is.
You try!
Use interval notation to represent the set of
numbers.
–6
–4
–2
0
2
4
6
There are two intervals graphed on the number line.
[–6, –4]
–6 and –4 are included.
(5, ∞)
5 is not included, and the interval
continues forever in the positive
direction.
[–6, –4] or (5, ∞)
The word “or” is used to indicate
that a set includes more than one
interval.
You try!
Use interval notation to represent each set of numbers.
a.
-4 -3 -2
(–∞, –1]
-1
0
1
2
3
4
–1 is included, and the interval continues
forever in the negative direction.
b. x ≤ 2 or 3 < x ≤ 11
(–∞, 2]
(3, 11]
2 is included, and the interval continues forever in the
negative direction.
3 is not included, but 11 is.
(–∞, 2] or (3, 11]
Set-builder notation: Use - Inequalities and the
element symbol
.
{9, 10, 11, 12, 13, 14, 15}.
The set of all numbers x such that x has the given properties
{x | 8 < x ≤ 15 and x  N}
Read the above as “the set of all numbers x
such that x is greater than 8 and less than or
equal to 15 and x is a natural number.”
Helpful Hint
The symbol  means “is an element of.” So x  N is read “x is an
element of the set of natural numbers,” or “x is a natural number.”
Ways to think of set notation
Interval Notation
Roster
Notation
Can only do
lists
Set-Builder Can only do
Notation
infinite intervals
Can do
BOTH
Example
Rewrite each set in the indicated notation.
A. {x | x > –5.5, x  Z }; words
integers greater than 5.5
B. positive multiples of 10; roster notation
{10, 20, 30, …} The order of elements is not important.
C.
-4 -3 -2
-1
{x | x ≤ –2}
0
1
; set-builder
2 3 4
notation
You Try !
Rewrite each set in the indicated notation.
a. {2, 4, 6, 8}; words
even numbers between 1 and 9
b. {x | 2 < x < 8 and x  N}; roster notation
{3, 4, 5, 6, 7}
The order of the elements is not
important.
c. [99, ∞}; set-builder notation
{x | x ≥ 99}
1.1 Activity: How Old is Mr. Xiong?!
Mr. Xiong’s age is in each of these sets. You must
read and decipher set notations to figure it out.
You should start with a large group of numbers
and can narrow it down each time by eliminating
certain numbers.
Summary :
1) Today we went over sets. A set is
_____________________________. A subset is
________
2) Three ways we can represent sets are …(give
examples)
3) Why can’t we use roster notation when dealing
with all the real numbers between 3 and 18 but could
when dealing with only natural numbers?
Revisit your learning targets
Evaluate your self on what we went ovwer in
class
Homework
• Hw : PG 10; 12-21, 26-39
- Work on the problems quietly with your
study group ( Study group expectations)
- Show all your work
Study Team Expectations
•
•
•
•
•
NO talking outside team
Keep voices down
Within team, keep conversations on math
Discuss questions w/team before calling the teacher
Explain and justify your ideas
More:
• Share ideas
• Ask questions/ offer help – don’t leave your teammates
behind
• Stop and verify answer
• Ask everyone before asking teacher
“What do I do when I’m Done?”
• Correct your mistakes on last night’s h/w.
• Do extension assignment and check your
answers
• Re-read notes from pervious lessons
• Help study team members
• Study for a re-take test/quiz
• Quiz yourself on old practice problems, quiz
• Do tonight's homework
Additional Notes
Methods
Roster
Notation
Interval
Notation
Set-Builder
Notation
Definition
Elements are listed
between brackets { }
Can only represent
lists of numbers
Elements are everything
between 2 endpoints using
( ) and [ ]. Can only
represent an infinite set of
numbers
Written in brackets { }
and given certain
properties.
It can represent both
lists and infinite sets.
Example
the set of natural
numbers:
{1, 2, 3, 4, 5…}
Or this random set:
{1, 4, 7, 15}
All numbers
between -2 and 3
and including 3:
(-2,3]
Natural Numbers:
{x I x is a natural
number}
All numbers between -2
and 3, including 3:
{x I -2<x<3}
Visual