Unit 1: Functions Lesson 4: Domain and Range Learning Goals: I can determine domains and ranges for tables, graphs, equations, and real world situations.

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


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


Whole Numbers – All the Natural Numbers, but also includes zero.

ex. 0, 1, 2, 3, …

We give them the symbol W.

Unit 1: Functions


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


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


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


Real Numbers - All Rational and Irrational Numbers.

We give them the symbol . (A fancy looking R).

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Unit 1: Functions


Set Notation - A collection of things, called elements

Example: The set notation for things in my pencil case is:

Unit 1: Functions


“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


We can use set notation to represent a set of numbers.

For example:

{ 1, 2, 3, 5, 7, 11, 13….}

Unit 1: Functions


We can also use set notation to represent all the possible values of a variable.

For Example:

{x

Unit 1: Functions


We can also list any restrictions using set notation.

For Example:

{g

To summarize:

{ variable | restriction(s), variable type }

Unit 1: Functions


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


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

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• The arrow indicates that all numbers bigger than 3 are included in this set

Unit 1: Functions


“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


Ex.

Can you graph it?

Unit 1: Functions


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


Unit 1: Functions


Unit 1: Functions


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


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


What restrictions would there be on our domain and range for this function?

Unit 1: Functions


Unit 1: Functions


Unit 1: Functions


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

Unit 1: Functions Lesson 4: Domain and Range Learning Goals: I can determine domains and ranges for tables, graphs, equations, and real world situations.

Documents

range unit

set unit

graphs unit

functions unit

set of numbers

rangereal numbers

rangewhole numbers

irrational numbers