Download 1.1 Sets of Numbers day 1.notebook

1.1 Sets of Numbers day 1.notebook
Algebra 2 Warm up 8/17/15
List or identify the following:
1. All the colors of the rainbow
2. All numbers between 1 and 25
3. Given the function f(x) = 2x ­ 1, evaluate when x = 1, 2, 3, 4
August 20, 2015
1.1 Sets of Numbers day 1.notebook
August 20, 2015
Chapter 1: Foundations for Functions
1.1: Sets of Numbers
Set: Element: A number (or thing) in the set Notation ­ symbols used to write a set of numbers. We will learn 3: 1) Roster Notation
2) Interval Notation
3) Set­Builder Notation
Roster Notation:
List of numbers of a set between braces { }
Ex: {1, 2, 3, 4, 5, 6, ...}
Infinite Set: A set with an unlimited, or
infinite, number of elements
Ex: A = {1, 2, 3, 4, 5, 6}
Finite Set: A set with a definite, or finite,
number of elements
1.1 Sets of Numbers day 1.notebook
August 20, 2015
In your groups...
Write the following sets of numbers in Roster Notation. Is the set finite or infinite? 1) All whole numbers between 7 and 12.
2) All positive multiples of 4.
3) All whole numbers within 3 units of 5.
4) All numbers including and between 3 and 6.
Algebra 2 Warm up 8/18/15
Write the following sets of numbers in Roster Notation.
1) All integers between ­3 and 3. 2) All multiples of 3 between 31 and 43.
1.1 Sets of Numbers day 1.notebook
August 20, 2015
Interval Notation:
A way of writing the set of
all real numbers (including decimals and fractions) between
two endpoints.
This notation is used for listing the infinite possibilities
between 2 numbers.
­10
­9
­8
­7
­6
­5
­4
­3
­2
­1
0
1
2
3
4
5
6
7
8
9
10
[ and ] - include an endpoint
( and ) - exclude an endpoint
x > 4
In your groups, write the interval notation for the following:
2 < x < 5
2 < x ≤ 5
2 ≤ x < 5
2 ≤ x ≤ 5
x ≤ 7 x > 3
1.1 Sets of Numbers day 1.notebook
August 20, 2015
Set -builder notation: A notation for a set that uses a
rule to describe the properties of the elements.
It looks like this:
{x| the rule goes here}
Ex: All numbers less than 3.
Ex: Positve multiples of 2
Natural Numbers are your counting numbers: 1, 2, 3, 4, ...
Converting from one notation to another
Interval Notation 1) [­3, 5) 2) (­5, 1]
3) (7, ∞)
4) (­∞, 5)
to Set­Builder Notation 1.1 Sets of Numbers day 1.notebook
Roster Notation August 20, 2015
to Set­Builder Notation 1) {3, 6, 9, 12, ...} 2) {7, 14, 21, 28, ...} 3) {­4, ­8, ­12, ­16, ...} 4) {6, 8, 10, 12, 14} Set­Builder Notation 1) {x| ­3 < x < 5} 2) {x| x ≥ 6} to Interval Notation
1.1 Sets of Numbers day 1.notebook
Set­Builder Notation August 20, 2015
to Roster Notation
1) {x| x = 3n + 1 and n ε N} 2) {x| x = 2n + 10 and n ε N, n < 7} Interval notation to roster notation. 1) [3, 8] 2) What about roster notation to interval notation?
{3, 4, 5, 6}
1.1 Sets of Numbers day 1.notebook
August 20, 2015
Real Numbers (r)
Rational Numbers (q )
Irrational Numbers
0.5
0.2222...
Integers (z)
..., ­3, ­2, ­1
√7
­2√2
Whole Numbers (w)
0
π
Natural Numbers (n )
7√3
1, 2, 3, 4, ...
e
1
32/5
/2
Rational numbers can be written as a fraction or repeating decimal.
Irrational numbers cannot be written as a fraction or repeating decimal, like π.
Real Numbers Rational Integers
Whole
Natural
Irrational
1.1 Sets of Numbers day 1.notebook
Classify. Put a check in all that apply. Write in order from least to greatest. August 20, 2015
1.1 Sets of Numbers day 1.notebook
August 20, 2015
HW #1: Signed syllabus with survey due Friday for extra credit
HW #2: Worksheet "Notation Chart" Sec. 1.1: p. 10 #2­4, 22­25