Unit 1: Functions Lesson 4: Domain and Range Learning Goals: I can determine domains and ranges for...
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Transcript of Unit 1: Functions Lesson 4: Domain and Range Learning Goals: I can determine domains and ranges for...
Unit 1: Functions
Lesson 4: Domain and Range
Learning Goals:
I can determine domains and ranges for tables, graphs, equations, and real world situations
I can describe domain and range using set notation.
Unit 1: Functions
Lesson 4: Domain and Range
Natural Numbers – These are the sort of numbers you can count on your fingers.
ex. 1, 2, 3,…
We give them the symbol N.
Unit 1: Functions
Lesson 4: Domain and Range
Whole Numbers – All the Natural Numbers, but also includes zero.
ex. 0, 1, 2, 3, …
We give them the symbol W.
Unit 1: Functions
Lesson 4: Domain and Range
Integer Numbers – or just Integers – All the Whole Numbers, including their negative versions. ex. …-3, -2, -1, 0, 1, 2, 3,…
We give them the symbol Z.
Unit 1: Functions
Lesson 4: Domain and Range
Rational Numbers – Any number that can be written as a fraction (Where a and b are both integers and b ) Rational numbers include all Natural, Whole and Integer numbers.
ex.
We give them the symbol Q.
Unit 1: Functions
Lesson 4: Domain and Range
Irrational Numbers – Any number that cannot be written as a fraction (Where a and b are both integers and b ) Numbers that do not terminate or repeat.
ex.
We give them the symbol Q.
Unit 1: Functions
Lesson 4: Domain and Range
Real Numbers - All Rational and Irrational Numbers.
We give them the symbol . (A fancy looking R).
Unit 1: Functions
Lesson 4: Domain and Range
Unit 1: Functions
Lesson 4: Domain and Range
Set Notation - A collection of things, called elements
Example: The set notation for things in my pencil case is:
Unit 1: Functions
Lesson 4: Domain and Range
“my pen" is an element of , and thus belongs to, the "Things in my Pencil Case" set
{“my pen“ “Things in My Pencil Case“}
Unit 1: Functions
Lesson 4: Domain and Range
We can use set notation to represent a set of numbers.
For example:
{ 1, 2, 3, 5, 7, 11, 13….}
Unit 1: Functions
Lesson 4: Domain and Range
We can also use set notation to represent all the possible values of a variable.
For Example:
{x
Unit 1: Functions
Lesson 4: Domain and Range
We can also list any restrictions using set notation.
For Example:
{g
To summarize:
{ variable | restriction(s), variable type }
Unit 1: Functions
Lesson 4: Domain and Range
The following example shows numbers that ARE included in a set:
• The closed dots indicate that 2 and 6 are included in the set.
• The straight brackets indicate the 2 and 6 are included in the set
Unit 1: Functions
Lesson 4: Domain and Range
The following example shows numbers that are NOT included in a set:
• The open dots indicate that 2 and 6 are not included in the set.
• The round brackets indicate the 2 and 6 are not included in the set
Unit 1: Functions
Lesson 4: Domain and Range
• The arrow indicates that all numbers bigger than 3 are included in this set
Unit 1: Functions
Lesson 4: Domain and Range
“The set of all values such that is greater than or equal to -2 and is less than or equal to 3. belongs to the set of integers.”
Ex.
What does that mean?
Unit 1: Functions
Lesson 4: Domain and Range
Ex.
Can you graph it?
Unit 1: Functions
Lesson 4: Domain and Range
Inequalities Symbols
> (greater than)
< (less than)
≤ (less than or equal to)
≥ (greater than or equal to)
(remember to read inequalities from left ---> right) ex: 5 > 2 means Five is greater than 2
Unit 1: Functions
Lesson 4: Domain and Range Determining Domain and Range from Graphs
Unit 1: Functions
Lesson 4: Domain and Range Determining Domain and Range from Graphs
Unit 1: Functions
Lesson 4: Domain and Range Determining Domain and Range from Graphs
Unit 1: Functions
Lesson 4: Domain and Range Determining Domain and Range from Graphs
Unit 1: Functions
Lesson 4: Domain and Range Determining Domain and Range from Equations – Linear
Y = -3x + 7
Unit 1: Functions
Lesson 4: Domain and Range Determining Domain and Range from Equations – Quadratic
f(x) = 2x2 – 3x + 1
Unit 1: Functions
Lesson 4: Domain and Range Determining Domain and Range from Equations – Square Root
f(x) =
Unit 1: Functions
Lesson 4: Domain and Range Determining Domain and Range from Equations – Reciprocal
f(x) =
Unit 1: Functions
Lesson 4: Domain and Range Sometimes there will be additional restrictions when our equations are representing real life situations.
Unit 1: Functions
Lesson 4: Domain and Range
Look at the following quadratic function. It represents the height of a football after it is kicked into the air. The height of the football, h(t) is measured in metres, and time, (t) is measured in seconds:
Let’s see where the ball is after 3 seconds:h(3) = -5(3)2 + 20(3)h(3) = -5(9) + 60h(3) = -45 + 60
h(3) = 15 m
Unit 1: Functions
Lesson 4: Domain and Range
What restrictions would there be on our domain and range for this function?
Unit 1: Functions
Lesson 4: Domain and Range
Unit 1: Functions
Lesson 4: Domain and Range
Unit 1: Functions
Lesson 4: Domain and Range
Homework
Level 4: Pg. 35-37 #1 – 11, 13-15 Level 3: Pg. 35-37 #1 – 11, 13 Level 2: Pg. 35-37 # 1 – 7 Level 1: Pg. 35-37 #1 - 4