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