Relations & Functions
Unlock your personalized study plan
PLEASE use the list below to unlock your personalized study plan for Relations & Functions. FOLLOW the PROMPTS TO SUPPORT YOUR MASTERY OF IMPORTANT ALGEBRAIC CONCEPTS.
START by taking Quiz 1 to identify your areas for growth. KA will recommend lessons for exactly what you need to learn. Use this link: https://www.khanacademy.org/math/algebra/algebra-functions#evaluating-functions
Follows in an outline of all components within the lesson. Please note that none of the Quiz links listed below are live; you must use the link above and click on the button/tab to complete the quizzes.
Evaluating functions
Learn
What is a function?
Worked example: Evaluating functions from equation
Worked example: evaluating functions from graph
Worked example: evaluating expressions with function notation
Practice
Evaluate functions
Evaluate functions from their graph
Evaluate function expressions
Inputs and outputs of a function
Learn
Worked example: matching an input to a function's output (equation)
Worked example: matching an input to a function's output (graph)
Worked example: two inputs with the same output (graph)
Practice
Function inputs & outputs: equation
Function inputs & outputs: graph
Functions and equations
Learn
Equations vs. functions
Obtaining a function from an equation
Practice
Function rules from equations
Quiz 1 Identify your areas for growth in these lessons:
Evaluating functions
Inputs and outputs of a function
Functions and equations
Interpreting function notation
Learn
Function notation word problem: bank
Function notation word problem: beach
Practice
Function notation word problems
Introduction to the domain and range of a function
Learn
Intervals and interval notation
What is the domain of a function?
What is the range of a function?
Worked example: domain and range from graph
Practice
Domain and range from graph
Determining the domain of a function
Learn
Domain of a radical function
Worked example: domain of algebraic functions
Worked example: determining domain word problem (real numbers)
Worked example: determining domain word problem (positive integers)
Worked example: determining domain word problem (all integers)
Practice
Determine the domain of functions
Function domain word problems
Recognizing functions
Learn
Recognizing functions from graph
Does a vertical line represent a function?
Recognizing functions from table
Recognizing functions from verbal description
Recognizing functions from verbal description word problem
Practice
Recognize functions from graphs
Recognize functions from tables
Quiz 2 Identify your areas for growth in these lessons:
Interpreting function notation
Introduction to the domain and range of a function
Determining the domain of a function
Recognizing functions
Maximum and minimum points
Learn
Introduction to minimum and maximum points
Worked example: relative maxima and minima
Practice
Relative maxima and minima
Absolute maxima and minima
Intervals where a function is positive, negative, increasing, or decreasing
Learn
Increasing, decreasing, positive or negative intervals
Worked example: positive & negative intervals
Practice
Positive and negative intervals
Increasing and decreasing intervals
Interpreting features of graphs
Learn
Graph interpretation word problem: temperature
Graph interpretation word problem: basketball
Practice
Graph interpretation word problems
Quiz 3 Identify your areas for growth in these lessons:
Maximum and minimum points
Intervals where a function is positive, negative, increasing, or decreasing
Interpreting features of graphs
Average rate of change
Learn
Introduction to average rate of change
Worked example: average rate of change from graph
Worked example: average rate of change from table
Worked example: average rate of change from equation
Practice
Average rate of change: graphs & tables
Average rate of change
Average rate of change word problems
Learn
Average rate of change word problem: table
Average rate of change word problem: graph
Average rate of change word problem: equation
Average rate of change review
Practice
Average rate of change word problems
Quiz 4 Identify your areas for growth in these lessons:
Average rate of change
Average rate of change word problems
Unit test Test your understanding of Functions with these 20 questions
==========================================================================================
Notes/Examples:
Functions
Vertical Line Test
Domain and Range
Function Notation
Functions
Quizlets:
Relations and Functions:
https://quizlet.com/435748665/algebra-1-functions-vocabulary-flash-cards/
https://quizlet.com/435663529/relations-and-functions-flash-cards/
https://quizlet.com/420710431/function-and-relation-flash-cards/
https://quizlet.com/389690502/function-or-relation-flash-cards/
Domain and range:
https://quizlet.com/427000024/domain-and-range-flash-cards/
https://quizlet.com/456051517/domain-range-flash-cards/?new
https://quizlet.com/421242732/domain-and-range-flash-cards/
https://quizlet.com/439606690/domain-and-range-flash-cards/
https://quizlet.com/324302993/domain-range-domain-and-range-flash-cards/
https://quizlet.com/318919527/domain-range-domain-and-range-flash-cards/
https://quizlet.com/405131232/domain-range-domain-and-range-flash-cards/
https://quizlet.com/423253817/domain-range-domain-and-range-flash-cards/
https://quizlet.com/456038469/domain-and-range-flash-cards/?new
Function Notation:
https://quizlet.com/420434101/function-notation-flash-cards/
https://quizlet.com/314638709/function-notation-flash-cards/
https://quizlet.com/413361079/function-notation-flash-cards/
Direct and Inverse Variation:
https://quizlet.com/460164943/direct-variation-note-constant-of-proportionality-is-the-same-as-constant-of-variation-just-as-directly-proportional-is-same-as-direct-variation-recall-ykx-when-k-is-the-constant-of-variation-flash-cards/?new
https://quizlet.com/326040461/direct-variation-flash-cards/
https://quizlet.com/250192051/direct-variation-flash-cards/
https://quizlet.com/446052523/direct-variation-flash-cards/
https://quizlet.com/293649518/direct-and-inverse-variation-flash-cards/
https://quizlet.com/462200876/direct-variation-inverse-variation-flash-cards/?new
https://quizlet.com/313779361/inverse-variation-flash-cards/
SelfChecks
http://www.phschool.com/webcodes10/index.cfm?wcprefix=ata&wcsuffix=0502&area=view
http://www.phschool.com/webcodes10/index.cfm?wcprefix=ata&wcsuffix=0503&area=view
http://www.phschool.com/webcodes10/index.cfm?wcprefix=ata&wcsuffix=0504&area=view
http://www.phschool.com/webcodes10/index.cfm?wcprefix=ata&wcsuffix=0505&area=view
http://www.phschool.com/webcodes10/index.cfm?wcprefix=ata&wcsuffix=0506&area=view
----------------------------------------------
https://www.youtube.com/watch?v=vO5qqfsWzhc#action=share
What is a function? | Functions and their graphs | Algebra II | Khan AcademyKhan Academy1,325,881 views
Relations & Functions
GAMES
Stop that Creature - Math Games for Kids . Cyberchase | PBS KIDS
Function Machine | MathPlayground.com
Fuzzy Functions The numbers at the Functions Factory are right, but the plus signs and minus signs are missing! Only you can help save the day!
Function Machine Investigate the relationship between input and output values in a function
Quia - All About Functions - Jeopardy Game
Vertical Line Test Learn about the vertical line test for functions by trying to connect points in the plane to build a function. When you have connected all of the points, you will be told if your graph is a valid graph of a function. Vertical Line Test is one of the Interactivate assessment explorers.
PLEASE use the list below to unlock your personalized study plan for Relations & Functions. FOLLOW the PROMPTS TO SUPPORT YOUR MASTERY OF IMPORTANT ALGEBRAIC CONCEPTS.
START by taking Quiz 1 to identify your areas for growth. KA will recommend lessons for exactly what you need to learn. Use this link: https://www.khanacademy.org/math/algebra/algebra-functions#evaluating-functions
Follows in an outline of all components within the lesson. Please note that none of the Quiz links listed below are live; you must use the link above and click on the button/tab to complete the quizzes.
Evaluating functions
Learn
What is a function?
Worked example: Evaluating functions from equation
Worked example: evaluating functions from graph
Worked example: evaluating expressions with function notation
Practice
Evaluate functions
Evaluate functions from their graph
Evaluate function expressions
Inputs and outputs of a function
Learn
Worked example: matching an input to a function's output (equation)
Worked example: matching an input to a function's output (graph)
Worked example: two inputs with the same output (graph)
Practice
Function inputs & outputs: equation
Function inputs & outputs: graph
Functions and equations
Learn
Equations vs. functions
Obtaining a function from an equation
Practice
Function rules from equations
Quiz 1 Identify your areas for growth in these lessons:
Evaluating functions
Inputs and outputs of a function
Functions and equations
Interpreting function notation
Learn
Function notation word problem: bank
Function notation word problem: beach
Practice
Function notation word problems
Introduction to the domain and range of a function
Learn
Intervals and interval notation
What is the domain of a function?
What is the range of a function?
Worked example: domain and range from graph
Practice
Domain and range from graph
Determining the domain of a function
Learn
Domain of a radical function
Worked example: domain of algebraic functions
Worked example: determining domain word problem (real numbers)
Worked example: determining domain word problem (positive integers)
Worked example: determining domain word problem (all integers)
Practice
Determine the domain of functions
Function domain word problems
Recognizing functions
Learn
Recognizing functions from graph
Does a vertical line represent a function?
Recognizing functions from table
Recognizing functions from verbal description
Recognizing functions from verbal description word problem
Practice
Recognize functions from graphs
Recognize functions from tables
Quiz 2 Identify your areas for growth in these lessons:
Interpreting function notation
Introduction to the domain and range of a function
Determining the domain of a function
Recognizing functions
Maximum and minimum points
Learn
Introduction to minimum and maximum points
Worked example: relative maxima and minima
Practice
Relative maxima and minima
Absolute maxima and minima
Intervals where a function is positive, negative, increasing, or decreasing
Learn
Increasing, decreasing, positive or negative intervals
Worked example: positive & negative intervals
Practice
Positive and negative intervals
Increasing and decreasing intervals
Interpreting features of graphs
Learn
Graph interpretation word problem: temperature
Graph interpretation word problem: basketball
Practice
Graph interpretation word problems
Quiz 3 Identify your areas for growth in these lessons:
Maximum and minimum points
Intervals where a function is positive, negative, increasing, or decreasing
Interpreting features of graphs
Average rate of change
Learn
Introduction to average rate of change
Worked example: average rate of change from graph
Worked example: average rate of change from table
Worked example: average rate of change from equation
Practice
Average rate of change: graphs & tables
Average rate of change
Average rate of change word problems
Learn
Average rate of change word problem: table
Average rate of change word problem: graph
Average rate of change word problem: equation
Average rate of change review
Practice
Average rate of change word problems
Quiz 4 Identify your areas for growth in these lessons:
Average rate of change
Average rate of change word problems
Unit test Test your understanding of Functions with these 20 questions
==========================================================================================
Notes/Examples:
Functions
Vertical Line Test
Domain and Range
Function Notation
Functions
Quizlets:
Relations and Functions:
https://quizlet.com/435748665/algebra-1-functions-vocabulary-flash-cards/
https://quizlet.com/435663529/relations-and-functions-flash-cards/
https://quizlet.com/420710431/function-and-relation-flash-cards/
https://quizlet.com/389690502/function-or-relation-flash-cards/
Domain and range:
https://quizlet.com/427000024/domain-and-range-flash-cards/
https://quizlet.com/456051517/domain-range-flash-cards/?new
https://quizlet.com/421242732/domain-and-range-flash-cards/
https://quizlet.com/439606690/domain-and-range-flash-cards/
https://quizlet.com/324302993/domain-range-domain-and-range-flash-cards/
https://quizlet.com/318919527/domain-range-domain-and-range-flash-cards/
https://quizlet.com/405131232/domain-range-domain-and-range-flash-cards/
https://quizlet.com/423253817/domain-range-domain-and-range-flash-cards/
https://quizlet.com/456038469/domain-and-range-flash-cards/?new
Function Notation:
https://quizlet.com/420434101/function-notation-flash-cards/
https://quizlet.com/314638709/function-notation-flash-cards/
https://quizlet.com/413361079/function-notation-flash-cards/
Direct and Inverse Variation:
https://quizlet.com/460164943/direct-variation-note-constant-of-proportionality-is-the-same-as-constant-of-variation-just-as-directly-proportional-is-same-as-direct-variation-recall-ykx-when-k-is-the-constant-of-variation-flash-cards/?new
https://quizlet.com/326040461/direct-variation-flash-cards/
https://quizlet.com/250192051/direct-variation-flash-cards/
https://quizlet.com/446052523/direct-variation-flash-cards/
https://quizlet.com/293649518/direct-and-inverse-variation-flash-cards/
https://quizlet.com/462200876/direct-variation-inverse-variation-flash-cards/?new
https://quizlet.com/313779361/inverse-variation-flash-cards/
SelfChecks
http://www.phschool.com/webcodes10/index.cfm?wcprefix=ata&wcsuffix=0502&area=view
http://www.phschool.com/webcodes10/index.cfm?wcprefix=ata&wcsuffix=0503&area=view
http://www.phschool.com/webcodes10/index.cfm?wcprefix=ata&wcsuffix=0504&area=view
http://www.phschool.com/webcodes10/index.cfm?wcprefix=ata&wcsuffix=0505&area=view
http://www.phschool.com/webcodes10/index.cfm?wcprefix=ata&wcsuffix=0506&area=view
----------------------------------------------
https://www.youtube.com/watch?v=vO5qqfsWzhc#action=share
What is a function? | Functions and their graphs | Algebra II | Khan AcademyKhan Academy1,325,881 views
Relations & Functions
- How is a Function Defined?
You can't go through algebra without learning about functions. This tutorial shows you the definition of a function and gives you an example of a function. Take a look!
What's a Function?You can't go through algebra without learning about functions. This tutorial shows you a great approach to thinking about functions! Learn the definition of a function and see the different ways functions can be represented. Take a look!
Introduction to Algebra Functions and Relations - Algebra help
Representing functions as rules and graphs (Algebra 1, Discovering ... www.mathplanet.com/.../algebra...expressions...functions/representing-functions-as-ru... Another word for input is domain and for output the range.
How Do You Find the Domain and Range of a Relation? | Virtual Nerd Finding the domain and range of a relation? No problem! Watch this tutorial and learn how to find the domain and range of a relation DiXi & RoYd What's a Function (Intro to Domain and Range) DiXi & RoYd
What is Domain? Did you know that a relation has a domain? The domain of a relation is the set of the first coordinates from the ordered pairs. This tutorial defines the domain of a relation! DiXi
What is the Range of a Relation? Did you know that a relation has a range? The range of a relation is the set of the second coordinates from the ordered pairs. This tutorial defines the range of a relation! RoYd
What Are Dependent and Independent Variables? Note: DiXi & RoYd
Notes: Domain and Range - notes and interactives from Purplemath.com Note: DiXi & RoYd
Notes: Functions - notes on functions, function boxes, domain and range, and mappings at Coolmath.com
Notes: Graphing Using a T-chart - notes on graphing at Purplemath.com
Linear equations in the coordinate plane How to use a general domain to determine range given a rule. Apply domain and range to graph.
Video: PH Modeling a Function Using Three Views
Video: PH Making a Table from a Function Rule
Video: PH Graphing a function using a table
Video: PH Finding the Range of a Function Given the Domain Note: DiXi & RoYd
Video: PH Writing a Rule from a Table
Video: PH Analyzing Linear Graphs
Video: PH Real-World Situations with Linear Equation
Video: PH Determining a Reasonable Domain and Range for a Situation Note: DiXi & RoYd - How Do You Find f(x) If You Have a Value For x? (note: f(x) represents the range value; in other words it is the same as y). (x,y) = (x,f(x))
To solve a function for a given value, plug that value into the function and simplify. See this first-hand by watching this tutorial!
How Do You Solve a Word Problem Using a Function?
Word problems are a great way to see math in action! This word problem deals with calculating profit after a certain number of years. See how to use a function from the word problem to solve!
Interactive: Function Machine - explore the concept of a function machine by inputting values and observing the output in a table at matti.usu.edu.
Interactive: Function Machine - investigate simple linear functions by trying to guess the algebraic form from inputs and outputs at Shodor.org.
Interactive: Function Machine - investigate simple linear functions by trying to guess the algebraic form from inputs and outputs at Shodor.org.
Interactive: Vertical Line Test - discovery activity that determines if a graph is a function at Shodor.org.
Interactive: Graphs and Functions - view images of graphs at Shodor.org and determine if they represent a function
Game:
Quia - Pre-Algebra Functions/Sequences Review - HOLT
Others:
Video: PH Identifying Functions using a Mapping
Video: PH Identifying Functions using a Vertical Line Test
GAMES
Stop that Creature - Math Games for Kids . Cyberchase | PBS KIDS
Function Machine | MathPlayground.com
Fuzzy Functions The numbers at the Functions Factory are right, but the plus signs and minus signs are missing! Only you can help save the day!
Function Machine Investigate the relationship between input and output values in a function
Quia - All About Functions - Jeopardy Game
Vertical Line Test Learn about the vertical line test for functions by trying to connect points in the plane to build a function. When you have connected all of the points, you will be told if your graph is a valid graph of a function. Vertical Line Test is one of the Interactivate assessment explorers.