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Algebra 2

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Transformations

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Shifting Functions

How to Solve Compound Inequalities and Learn About Disconnected Domain and Range

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How to Solve Compound Inequalities and Learn About Disconnected Domain and Range
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Shea McDonough

@heaconough_jlyx

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A comprehensive guide to mathematical functions and transformations, focusing on inequalities, domains, and graphing techniques. This material covers essential concepts for understanding كيفية حل المتباينات المركبة and دوال نطاق ومدى غير متصلة.

  • Complex inequalities and their solutions, including intersection and union concepts
  • Domain and range analysis for discrete and continuous functions
  • Function transformations and parent functions
  • Slope calculations and linear equations in various forms
  • Special functions including quadratic, absolute value, and rational functions

9/18/2023

24

ن Solving ine If asb then atc4b+c and a-c²b-c b=5 4*858213 4-865-8-4²-3 If asb then ² ac cbc * if we multiply or divide by a negitive #. nee

View

Page 2: Relations and Functions

This section explores the fundamental concepts of relations and functions, focusing on domains, ranges, and the distinction between discrete and continuous relationships.

Definition: A function is a relation where each input (x-value) corresponds to exactly one output (y-value).

Example: The set {(5,3), (4,2), (3.1,1), (4,0)} represents a discrete relation.

Highlight: The vertical line test determines if a relation is a function - if a vertical line intersects the graph more than once, it's not a function.

Vocabulary: Domain represents input values, while range represents possible output values.

ن Solving ine If asb then atc4b+c and a-c²b-c b=5 4*858213 4-865-8-4²-3 If asb then ² ac cbc * if we multiply or divide by a negitive #. nee

View

Page 3: Function Notation and Forms

This chapter covers function notation and different forms of linear equations, incorporating صيغة الميل والمقطع العامية concepts.

Definition: Standard form: Ax + By = C Point-slope form: y - y₁ = m(x - x₁) Slope-intercept form: y = mx + b

Example: f(2) = 2² + 2(2) = 4 + 4 = 8 demonstrates function evaluation.

Highlight: When converting between forms, ensure there are no fractions in standard form and no common factors.

ن Solving ine If asb then atc4b+c and a-c²b-c b=5 4*858213 4-865-8-4²-3 If asb then ² ac cbc * if we multiply or divide by a negitive #. nee

View

Page 4: Slope and Linear Relationships

This section focuses on slope calculations and linear relationships between points, including parallel and perpendicular lines.

Definition: Parallel lines have the same slope, while perpendicular lines have opposite reciprocal slopes.

Example: Calculating slope using m = (y₂-y₁)/(x₂-x₁)

Vocabulary: Scatter plot represents data points graphed as ordered pairs.

Highlight: Regression lines can be calculated using statistical tools to analyze data relationships.

ن Solving ine If asb then atc4b+c and a-c²b-c b=5 4*858213 4-865-8-4²-3 If asb then ² ac cbc * if we multiply or divide by a negitive #. nee

View

Page 5: Parent Functions and Domains

This page covers parent functions and their domains, essential for understanding دوال نطاق ومدى غير متصلة.

Definition: Domain represents x-values for which a function is defined, while range represents possible y-values.

Example: For f(x) = √x, the domain is [0,∞) since square roots of negative numbers are undefined.

Highlight: Special attention must be paid to restrictions such as denominators equal to zero and negative values under square roots.

ن Solving ine If asb then atc4b+c and a-c²b-c b=5 4*858213 4-865-8-4²-3 If asb then ² ac cbc * if we multiply or divide by a negitive #. nee

View

Page 6: Function Transformations

This final section explores various function transformations and their effects on parent functions.

Definition: Transformations include reflections, translations, stretches, and compressions.

Example: f(x) = -|x| - 3 represents a reflection over the x-axis and a downward shift of 3 units.

Highlight: The order of transformations matters when applying multiple changes to a parent function.

ن Solving ine If asb then atc4b+c and a-c²b-c b=5 4*858213 4-865-8-4²-3 If asb then ² ac cbc * if we multiply or divide by a negitive #. nee

View

Page 1: Complex Inequalities

This page introduces solving complex inequalities and understanding intersection and union concepts. The material covers essential techniques for handling compound inequalities joined by "and/or" operators.

Definition: Complex inequalities are mathematical statements containing two or more inequalities joined by logical operators (AND/OR).

Example: For inequalities like -3≤2x+5≤19, solve each part separately and then combine the solutions based on the logical operator.

Highlight: When multiplying or dividing by a negative number, the inequality sign must be flipped to maintain the correct relationship.

Vocabulary: Intersection represents the overlap of two sets, while union combines all elements from both sets.

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SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

Subjects

/

Algebra 2

/

Transformations

/

Shifting Functions

How to Solve Compound Inequalities and Learn About Disconnected Domain and Range

user profile picture

Shea McDonough

@heaconough_jlyx

·

0 Follower

Follow

A comprehensive guide to mathematical functions and transformations, focusing on inequalities, domains, and graphing techniques. This material covers essential concepts for understanding كيفية حل المتباينات المركبة and دوال نطاق ومدى غير متصلة.

  • Complex inequalities and their solutions, including intersection and union concepts
  • Domain and range analysis for discrete and continuous functions
  • Function transformations and parent functions
  • Slope calculations and linear equations in various forms
  • Special functions including quadratic, absolute value, and rational functions

9/18/2023

24

 

10th/11th

 

Algebra 2

2

ن Solving ine If asb then atc4b+c and a-c²b-c b=5 4*858213 4-865-8-4²-3 If asb then ² ac cbc * if we multiply or divide by a negitive #. nee

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 2: Relations and Functions

This section explores the fundamental concepts of relations and functions, focusing on domains, ranges, and the distinction between discrete and continuous relationships.

Definition: A function is a relation where each input (x-value) corresponds to exactly one output (y-value).

Example: The set {(5,3), (4,2), (3.1,1), (4,0)} represents a discrete relation.

Highlight: The vertical line test determines if a relation is a function - if a vertical line intersects the graph more than once, it's not a function.

Vocabulary: Domain represents input values, while range represents possible output values.

ن Solving ine If asb then atc4b+c and a-c²b-c b=5 4*858213 4-865-8-4²-3 If asb then ² ac cbc * if we multiply or divide by a negitive #. nee

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 3: Function Notation and Forms

This chapter covers function notation and different forms of linear equations, incorporating صيغة الميل والمقطع العامية concepts.

Definition: Standard form: Ax + By = C Point-slope form: y - y₁ = m(x - x₁) Slope-intercept form: y = mx + b

Example: f(2) = 2² + 2(2) = 4 + 4 = 8 demonstrates function evaluation.

Highlight: When converting between forms, ensure there are no fractions in standard form and no common factors.

ن Solving ine If asb then atc4b+c and a-c²b-c b=5 4*858213 4-865-8-4²-3 If asb then ² ac cbc * if we multiply or divide by a negitive #. nee

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 4: Slope and Linear Relationships

This section focuses on slope calculations and linear relationships between points, including parallel and perpendicular lines.

Definition: Parallel lines have the same slope, while perpendicular lines have opposite reciprocal slopes.

Example: Calculating slope using m = (y₂-y₁)/(x₂-x₁)

Vocabulary: Scatter plot represents data points graphed as ordered pairs.

Highlight: Regression lines can be calculated using statistical tools to analyze data relationships.

ن Solving ine If asb then atc4b+c and a-c²b-c b=5 4*858213 4-865-8-4²-3 If asb then ² ac cbc * if we multiply or divide by a negitive #. nee

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Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 5: Parent Functions and Domains

This page covers parent functions and their domains, essential for understanding دوال نطاق ومدى غير متصلة.

Definition: Domain represents x-values for which a function is defined, while range represents possible y-values.

Example: For f(x) = √x, the domain is [0,∞) since square roots of negative numbers are undefined.

Highlight: Special attention must be paid to restrictions such as denominators equal to zero and negative values under square roots.

ن Solving ine If asb then atc4b+c and a-c²b-c b=5 4*858213 4-865-8-4²-3 If asb then ² ac cbc * if we multiply or divide by a negitive #. nee

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 6: Function Transformations

This final section explores various function transformations and their effects on parent functions.

Definition: Transformations include reflections, translations, stretches, and compressions.

Example: f(x) = -|x| - 3 represents a reflection over the x-axis and a downward shift of 3 units.

Highlight: The order of transformations matters when applying multiple changes to a parent function.

ن Solving ine If asb then atc4b+c and a-c²b-c b=5 4*858213 4-865-8-4²-3 If asb then ² ac cbc * if we multiply or divide by a negitive #. nee

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 1: Complex Inequalities

This page introduces solving complex inequalities and understanding intersection and union concepts. The material covers essential techniques for handling compound inequalities joined by "and/or" operators.

Definition: Complex inequalities are mathematical statements containing two or more inequalities joined by logical operators (AND/OR).

Example: For inequalities like -3≤2x+5≤19, solve each part separately and then combine the solutions based on the logical operator.

Highlight: When multiplying or dividing by a negative number, the inequality sign must be flipped to maintain the correct relationship.

Vocabulary: Intersection represents the overlap of two sets, while union combines all elements from both sets.

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Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying