About Us

Why Choose StudyPug

How it works

Pricing

Testimonials

Contact Us

Blog

Basic Math

Algebra

Geometry

Trigonometry

Calculus

Linear Algebra

Differential Equations

Statistics

Chemistry

Organic Chemistry

Physics

Microeconomics

For Students

For Parents

For Home Schoolers

For Teachers

Australia

Canada

Ireland

New Zealand

Singapore

United Kingdom

United States

Sitemap

Terms of Service

Privacy Policy

Domain and Range of Functions: Mastering Key Concepts

EQAO Grade 9 Math: Master Core Concepts & Skills

Ratios, Rates, and Proportions

test

auto-gen

Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Unit Rate

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

Square Roots

Squares and square roots

Square Root of a Perfect Square

Estimating square roots

Pythagorean Theorem

Introduction to pythagorean theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Rational Numbers

Comparing and ordering rational numbers

Comparing decimal numbers

Comparing fractions

Solving problems with rational numbers in decimal form

Mixed Operations with Decimals

Mixed Operations

Mixed Operations with Decimals Bracket

Mixed Operations with Bracket Square

Solving problems with rational numbers in fraction form

Operations with fractions

Determine square roots of rational numbers

Square roots of rational numbers

Powers and Exponents

Using exponents to describe numbers

Expanded powers

Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Using exponents to solve problems

Proportional Relationships

Understanding graphs of proportional relationships

Linear relations

Using tables of values to graph proportional relationships

Linear relation

Applications of proportional relationships

Identifying proportional relationships

Linear Ralations

Representing patterns in linear relations

Represent Patterns in Linear Relations Equation Decimal

Represent Patterns in Linear Relations Equation Integer Start From 0

Represent Patterns in Linear Relations Equation Integer Start From 1

Represent Patterns in Linear Relations Equation Negative Decimal

Identify the Linear Equation

Reading linear relation graphs

Solving linear equations by graphing

Solving Linear Equations

Solving linear equations using multiplication and division

Two-step Linear Equations LHS

Two-step Linear Equations RHS

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations with variables on both sides

Introduction to Relations and Functions

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Linear Functions

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Slope intercept form: y = mx + b

General form: Ax + By + C = 0

Point-slope form: \(y - y_1 = m (x - x_1)\)

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

Introduction to Polynomials

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

Multiplication and Division of Polynomials

Multiplying and dividing monomials 

Divide a monomial by a monomial

Multiply a monomial by a monomial

Multiplying polynomials by monomials

Multiply a polynomial by a monomial

Dividing polynomials by monomials

Introduction to 3-Dimensional Objects

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface Area of Prisms Rectangle

Calculate the Surface Area

Surface area of cylinders

Surface Area and Volume

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Circle Geometry

Angles in a circle

Chord properties 

Tangent properties

Data Management

Influencing factors in data collection

Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Sampling methods

Sampling Methods

Scatter plots and correlation

Census and bias

Census and Bias

Classifying Bias

Linear Programming

What is linear programming?

Finding Optimal Values Given Constraints In Slope-Intercept Form

Finding Optimal Values Given Constraints In Standard Form

Linear programming word problems

EQAO Grade 9 Principles of Math

sample

math

https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-ca-eqao-9-principles-math.png

Intro

Ex 1: 

a.) 

b.) 

c.) 

- Hi, welcome to this question right here. So we're trying to figure out the domain, the range, again, to see whether the function or not. So the domain for this one's a little tricky, because it seems to start specifically at this point right here. So if I'm gonna do a domain down here, I am going to say that it's starting from a negative three and towards the right infinitely. So how do I do that in terms of domain? Well, there's a couple different ways. I can write down my X is greater than or equal to, because that's a closed dot, okay? And there's a difference between a closed dot and an open dot. So in this case, the X is greater than or equal to the negative three, okay? You can also do it this way: You can also draw something like a square bracket, and you can put down a negative three. It means you start at a negative three, okay? You start on the left hand side, negative three, and it's a square bracket because it represents it also includes the negative three, and the little comma right here, but the problem is the graph extends toward the right infinitely, right? So you just have to do that little infinitely sign, okay? And you do an open bracket, okay? A curved bracket, sorry. So this kind of means that it goes on and on and on forever. It doesn't stop, okay? So there's two ways to write your domain in this case. There's, I believe this is called the interval, and the other one's called a set. And what about the range? 
The range is the same thing, but this, I'm gonna look at the y-axes, right? So if you look at the y direction, it seems like you started at the negative two, and then it goes up infinitely, because there's the arrowhead. So I could do: My Y's gonna be greater and equal to a negative two, or I can also do what I just did here for the-- 
the set notation. It's gonna be starting on the negative two. Again, a square bracket, because it includes the negative two, and again it goes on infinitely, so I'm gonna do a little curved bracket right here meaning it doesn't stop. It goes on infinitely to the top. And lastly you're supposed to determine whether it's a function or not. So, again, vertical line test. So I'm gonna call it the "vertical line test. " The vertical line test. A VLT, okay? What does that mean? It means you take your pen or pencil, straight, hold it vertically, straight up, and then you just have to move it across. Once it starts touching your function, which is your graph, as long as it touches once as it moves across, then it is still a function, okay? 
So in this case, it passed my vertical line test, so therefore it is a function. Okay? Does that make sense? 
Thanks for watching.

d.) 

e.) 

f.) 

g.) 

h.) 

i.) 

The domain of a function is all the possible values of x's of ordered pairs; whereas the range of a function is all the possible values of y's of ordered pairs. You can easily find them by graphing the functions or ordered pairs. Let's see how in this lesson.

What is the domain and range of a function?