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Domain and Range of Functions: Mastering Key Concepts

Demonstrate understanding of linear relations

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Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying 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

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Function notation

Parallel and perpendicular lines in linear functions

Applications of linear relations

Solve problems using sine law and cosine law

Introduction to bearings

Bearings and direction word problems

Bearings and Direction Word Problems

Angle of elevation and depression

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Solve problems involving triangles, quadrilaterals, and regular polygons

Similar triangles

Similar polygons

Classifying triangles

Isosceles and equilateral triangles

Demonstrate understanding of transformations on 2-D shapes and 3-D objects

Line symmetry

Rotational symmetry and transformations

Enlargements and reductions with scale factors

Scale diagrams

Demonstrate understanding of limitations of measuring instruments

Conversions between metric and imperial systems

Metric to Imperial Conversions

Imperial to Metric Conversions

Conversions Between Metric and Imperial Systems Speed KM to MI

Conversions Between Metric and Imperial Systems Speed  MI to M

Metric-Imperial Length Conversion Inch To Cm

Metric-Imperial Length Conversion MM/CM/M/KM To FT

Metric-Imperial Length Conversion MM/CM/M/KM To MI

Metric systems

Add and Subtract Mixed Units

Metric Length Conversion

Add or Subtract Different Metric Units Convert to CM

Add or Subtract Different Metric Units Convert to M

Add or Subtract Different Metric Units Convert to MM

Imperial systems

Imperial Length Conversion

Conversions involving squares and cubic

Imperial to Metric Conversions — Squares and Cubes

Imperial Conversion — Squares and Cubes

Metric to Imperial Conversion — Squares and Cubes

Metric Area Conversion FT to CM

Metric Area Conversion Foot to Inch

Metric Area Conversion M/CM to Inch

Analyze puzzles and games involving logical reasoning

Addition rule for "OR"

Addition Rule for "OR"

Multiplication rule for "AND"

Multiplication Rule for "AND"

Conditional probability

Probability involving permutations and combinations

Solve problems involving vehicle acquisition by buying, leasing, and leasing to buy

Simple interest

Simple Interest — Word Problem

Basic Concepts of Simple Interest – Word Problem

Borrowing Money for More Than One Year  – Word Problem

Investigate the Advantages of Borrowing Money  – Word Problem

Finance: Future value and present value

Critique viability of small business options considering expenses, sales, profit or loss

Taxes, discounts, tips and more

Discounts — Word Problem

Taxes — Word Problem

Percentage - Applying a Discount Price– Word Problem

Percentage - Applying a Discount Percent – Word Problem

Percentage - Applying a Tax Total – Word Problem

Percentage - Applying a tax Percent – Word Problem

Analyze and interpret problems involving probability

Introduction to probability

Identify the Probability — Word Problem

Compound Probability

Reading Probability Models

Probability

Organizing outcomes

Calculating Outcomes

Probability of independent events

Comparing experimental and theoretical probability

comparing experimental and theoretical probability

Solve problems involving measures of central tendency

Median and mode

Median and Mode Table

Median and Mode – Word Problem

Median of an even length list

Median of an odd length list

Mean

Mean Word Problems

Find the Mean

Application of Means

Range and outliers

Range and Outlier Word Problems

Outlier Word Problems

Range Word Problems

Find the Range

Application of averages

Measures of Central Tendency — Word Problem

Find the Means — Data Tables

Find Mean and Mode — Data Table

Identify Outliers — Data Table

Analyze and describe percentiles

Measures of relative standing - z-score, quartiles, percentiles

Mathematics at Work 12

Measurement

Number

math

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?

Draw on coordinate planes

Horizontal and vertical distances