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# Relations and Functions Mind Map

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#### Transcript of Relations and Functions Mind Map

RELATIONS

AND

FUNCTIONS RELATIONS Functions Definition: A connection between two objects of two sets A relationship between values, where

each element in the domain

is linked to exactly one element

in the range There are various ways to show relations As a Table :) (Not THIS kind of table...) As a set of ordered pairs Write the relation in words As an Arrow Diagram (Image credit: http://media.nlsd113.org/picture/Domain-and-Range--Arrow-Diagram/0c2965dd5607ad0deca58e39660f1d66) Example: The relations shows “has the number of wheels” between the set of vehicles and the set of numbers. Example: ( "Pairs" not "PEARS" Example: {(motorbike, 2), (trike, 3), (quad,4), (UTV,4)} Example: Linear Relation A constant change in the independent variable results in a constant change in the dependent variable Dependent variable= (rate of change) (independent variable) + initial value

AKA: y=mx +b Constant change in the indepentdent variable

=

Constant change in the dependent variable Example: (Image Credit:

http://www.utdanacenter.org/mathtoolkit/instruction/activities/alg1.php) Rate Of Change How to calculate the rate of change:

Divide the dependent variable

by the independent variable

AKA: change in y ÷ change in x

AKA: slope Example:

It costs $5 for 500cm of cloth.

*rate of change in dependent variable: +500cm

*rate of change in independent variable: = +5

500 ÷ 5 = 100

So, the rate of change is 100cm/dollar. [Example created by me.] No two points on the graph of a function will have the same x-value Example: (Image credits:

http://www.chegg.com/homework-help/questions-and-answers/q1-sum-integral-multiples-6-5-to99-use-formula-sum-theseries--q2-functions-set-rsquo-x-rsq-q856783

http://www.chegg.com/homework-help/questions-and-answers/q1-sum-integral-multiples-6-5-to99-use-formula-sum-theseries--q2-functions-set-rsquo-x-rsq-q856783 Linear Function:

an equation which makes a straight line on a graph, that is not vertical Example: Credit:

http://www.icoachmath.com/math_dictionary/Linear_Function.html 1st set of elements: Domain, x values independent variable

2nd set of elements: Range, y values, dependent variable Graphs Credit: http://www.mathcomposer.com/Graphs.htm If the values are limited to discrete values, the points are not connected Continuous Graphs

Example: Credit: http://catalog.flatworldknowledge.com/bookhub/reader/4372?e=fwk-redden-ch07_s02 Discrete Graphs Example: Credit: http://www.mathplanet.com/education/algebra-1/visualizing-linear-functions/linear-equations-in-the-coordinate-plane You can check if a relation is a linear function with a graph...

The line will be straight, but never vertical Credit:

http://www.wyzant.com/help/math/algebra/functions Not a linear function By: Maria Yanagisawa

F&P 10

Block 3

February 2013

Full transcriptAND

FUNCTIONS RELATIONS Functions Definition: A connection between two objects of two sets A relationship between values, where

each element in the domain

is linked to exactly one element

in the range There are various ways to show relations As a Table :) (Not THIS kind of table...) As a set of ordered pairs Write the relation in words As an Arrow Diagram (Image credit: http://media.nlsd113.org/picture/Domain-and-Range--Arrow-Diagram/0c2965dd5607ad0deca58e39660f1d66) Example: The relations shows “has the number of wheels” between the set of vehicles and the set of numbers. Example: ( "Pairs" not "PEARS" Example: {(motorbike, 2), (trike, 3), (quad,4), (UTV,4)} Example: Linear Relation A constant change in the independent variable results in a constant change in the dependent variable Dependent variable= (rate of change) (independent variable) + initial value

AKA: y=mx +b Constant change in the indepentdent variable

=

Constant change in the dependent variable Example: (Image Credit:

http://www.utdanacenter.org/mathtoolkit/instruction/activities/alg1.php) Rate Of Change How to calculate the rate of change:

Divide the dependent variable

by the independent variable

AKA: change in y ÷ change in x

AKA: slope Example:

It costs $5 for 500cm of cloth.

*rate of change in dependent variable: +500cm

*rate of change in independent variable: = +5

500 ÷ 5 = 100

So, the rate of change is 100cm/dollar. [Example created by me.] No two points on the graph of a function will have the same x-value Example: (Image credits:

http://www.chegg.com/homework-help/questions-and-answers/q1-sum-integral-multiples-6-5-to99-use-formula-sum-theseries--q2-functions-set-rsquo-x-rsq-q856783

http://www.chegg.com/homework-help/questions-and-answers/q1-sum-integral-multiples-6-5-to99-use-formula-sum-theseries--q2-functions-set-rsquo-x-rsq-q856783 Linear Function:

an equation which makes a straight line on a graph, that is not vertical Example: Credit:

http://www.icoachmath.com/math_dictionary/Linear_Function.html 1st set of elements: Domain, x values independent variable

2nd set of elements: Range, y values, dependent variable Graphs Credit: http://www.mathcomposer.com/Graphs.htm If the values are limited to discrete values, the points are not connected Continuous Graphs

Example: Credit: http://catalog.flatworldknowledge.com/bookhub/reader/4372?e=fwk-redden-ch07_s02 Discrete Graphs Example: Credit: http://www.mathplanet.com/education/algebra-1/visualizing-linear-functions/linear-equations-in-the-coordinate-plane You can check if a relation is a linear function with a graph...

The line will be straight, but never vertical Credit:

http://www.wyzant.com/help/math/algebra/functions Not a linear function By: Maria Yanagisawa

F&P 10

Block 3

February 2013