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Domain and Range of Functions: Mastering Key Concepts

CC.HSA.REI.C.8

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Notation of matrices

Adding and subtracting matrices

Scalar multiplication of matrices

Representing a linear system as a matrix

CC.HSA.REI.C.9

Matrix multiplication

The three types of matrix row operations

The Inverse of a 2 x 2 matrix

Solving linear systems using 2 x 2 inverse matrices

CC.HSA.SSE.B.4

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Geometric series

Geometric Series

CC.HSF.BF.A.2

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Geometric sequences

Infinite geometric series

CC.HSF.BF.B.4

Finding the quadratic functions for given parabolas

Inverse functions

CC.HSF.IF.A.1

Domain and range of a function

Identifying functions

Function notation (advanced)

CC.HSF.IF.A.2

Function notation

Difference quotient: applications of functions

CC.HSF.IF.A.3

Greatest common factors (GCF)

Greatest Common Factor 2 Numbers

Greatest Common Factor 2 Numbers – Word Problem

Introduction to sequences

Sigma notation

CC.HSF.IF.B.5

Point of discontinuity

Even and odd functions

CC.HSF.LE.A.2

Graphing linear functions using table of values

CC.HSN.VM.A.1

Use sine ratio to calculate angles and sides (Sin = o / h)

Introduction to vectors

Magnitude of a vector

Direction angle of a vector

CC.HSN.VM.A.2

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

Scalar multiplication of vectors

Equivalent vectors

CC.HSN.VM.B.4

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>

Adding and subtracting vectors in component form

Operations on vectors in magnitude and direction form

CC.HSN.VM.B.5

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

Unit vector

CC.HSN.VM.C.10

Zero matrix

Identity matrix

The determinant of a 2 x 2 matrix

The determinant of a 3 x 3 matrix (General & Shortcut Method)

CC.HSN.VM.C.11

Transforming vectors with matrices

Transforming shapes with matrices

CC.HSN.VM.C.6

CC.HSN.VM.C.9

Properties of matrix multiplication

CC.HSS.CP.A.1

Set notation

Understanding How to Use Set Notation

Set builder notation

Intersection and union of 2 sets

Intersection and Union of 2 Sets

Intersection and union of 3 sets

Intersection and Union of 3 Sets

Introduction to probability

Identify the Probability — Word Problem

Compound Probability

Reading Probability Models

Probability

Organizing outcomes

Calculating Outcomes

CC.HSS.CP.A.2

Probability of independent events

Multiplication rule for 

Multiplication rule for "AND"

Multiplication Rule for "AND"

CC.HSS.CP.A.3

Conditional probability

CC.HSS.CP.A.5

Comparing experimental and theoretical probability

comparing experimental and theoretical probability

CC.HSS.CP.B.9

Permutations

Combinations

Probability involving permutations and combinations

CC.HSS.IC.A.1

Sampling methods

Sampling Methods

CC.HSS.IC.B.3

Census and bias

Census and Bias

Classifying Bias

CC.HSS.IC.B.4

Margin of error

Margin of Error

Making a confidence interval

Confidence intervals to estimate population mean

CC.HSS.ID.A.2

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

Center of a data set: mean, median, mode

Spread of a data set - standard deviation & variance

CC.HSS.ID.A.3

Application of averages

Measures of Central Tendency — Word Problem

Find the Means — Data Tables

Find Mean and Mode — Data Table

Identify Outliers — Data Table

Shapes of distributions

CC.HSS.MD.A.1

Probability distribution - histogram, mean, variance & standard deviation

CC.HSS.MD.A.2

Properties of expectation

Properties of Expectation and Variance

Properties of Expectation

CC.HSS.MD.A.3

Binomial distribution

Binomial Distribution

Mean and standard deviation of binomial distribution

Interpreting Mean and Standard Deviation of Binomial

CC.HSS.MD.B.7

Type 1 and type 2 errors

Type 1 and Type 2 Errors

Discrete Mathematics/Computer Science

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.) 