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Domain and Range of Functions: Mastering Key Concepts

Demonstrate an understanding of factors of whole numbers

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Prime factorization

Number properties: Prime or Composite

Number properties: Prime?

Prime factors – Word Problem

Greatest common factors (GCF)

Greatest Common Factor 2 Numbers

Greatest Common Factor 2 Numbers – Word Problem

Least common multiple (LCM)

Lowest Common Multiple - 2 Numbers – Word Problem

Lowest Common Multiple 2 Numbers

Square and square roots

Square Root of a Perfect Square

Cubic and cube roots

Cube root of a perfect cube

Demonstrate an understanding of irrational numbers

Evaluating and simplifying radicals

Rational vs. Irrational numbers

Converting radicals to mixed radicals

Converting radicals to entire radicals

Demonstrate an understanding of powers with integral and rational exponents

Product rule of exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Simplify the power

Negative exponent rule

Combining the exponent rules

Scientific notation

Convert between radicals and rational exponents

Demonstrate an understanding of multiplication of polynomial expressions

Multiplying monomial by monomial

Multiply a Monomial by a Monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Applications of polynomials

Demonstrate an understanding of common factors and trinomial factoring

Factoring polynomials: ax^2 + bx + c

Factoring Polynomials: ax^2 + bx + c

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Factoring perfect square trinomials

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Find the difference of squares

Word problems of polynomials

Common factors of polynomials

Factoring polynomials by grouping

Factoring polynomials: x^2 + bx + c

Interpret and explain the relationships among data, graphs and situations

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Solve problems involving systems of linear equations in two variables

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

Factoring trinomials

Factoring Trinomials

Demonstrate an understanding of relations and functions

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

Demonstrate an understanding of slope

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>

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Rate of change

Describe and represent linear relations

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

General form:  Ax  + By  + C = 0

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

Determine the characteristics of the graphs of linear relations

Introduction to linear equations

Introduction to nonlinear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

Parallel and perpendicular lines in linear functions

Relate linear relations expressed in various forms

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Applications of linear relations

Applications of linear equations

Solving systems of linear equations by elimination

Determine the equation of a linear relation

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Solving systems of linear equations by substitution

Solve problems involving distance between two points and midpoint of a line segment

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>

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

Use cosine ratio to calculate angles and sides (Cos = a / h)

Use tangent ratio to calculate angles and sides (Tan = o / a)

Represent a linear function using function notation

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Number Relations and Functions 10

Algebra and Number

Relations and Functions

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