IMPORTANT VOCABULARY RELATION- a relation between mathematical expressions (EXAMPLE: number of cookies to cups of milk) FUNCTION- a relation of such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function) DOMAIN- the set of values of the independent variable for which a function is defined(EXAMPLE: number of cookies) RANGE- the set of values of the dependent variable for which a function is defined(EXAMPLE: cups of milk) INDEPENDENT VARIABLE-
the variable we change in order to measure our output(EXAMPLE: number of cookies) DEPENDENT VARIABLE-
the variable that changes based on the value that is chosen for the input (EXAMPLE: cups of milk) DISCRETE VARIABLES- Variables that only represent incremental values CONTINUOUS VARIABLES- Variables that represent all numbers along an interval SPECIAL CASE- If all the variables are possible, the domain and range could be "All real numbers"
REPRESENTING DOMAIN AND RANGE: Discrete Variables: Use set notation! Ex: {(2,0,1)} *Domain and Range for discrete variables should be in numerical or alphabetical order! Continuous Variables: Use interval Notation!
The 5 Different Representations of Relations
- Mapping Diagrams
-Graphs
-Tables
-Ordered Pairs
-Equations
BIG IDEAS FIVE DIFFERENT REPRESENTATIONS OF MAPPING the five different representations of mapping are mapping diagrams, tables, ordered pairs, graphs and equasions WHAT IS A FUNCTION? a special relation where each input only has one output. No values of the domain can repeat. "The output is a function of the input" DISCRETE VARIABLES variables that only represent incremental values EXAMPLE: number of people, states CONTINUOUS VARIABLES variables that represent all numbers(fractions and decimals) along an interval EXAMPLE: time, money REPRESENT DOMAIN AND RANGE DISCRETE- variables use set notation {-2,0,1} *domain and range for discrete variables should be in numerical or alphabetical order CONTINUOUS-variables use sinterval notation 0<x<12 SPECIAL CASE If all values are possible, the domain or range could be "all real numbers" R=all real numbers
REAL WORLD PROBLEMS The amount of people in a house depends on the amount of bedrooms.
The amount of flowers in a 4ft by 4ft square depends of the size of the flowers.
IMPORTANT VOCABULARY
RELATION-
a relation between mathematical expressions (EXAMPLE: number of cookies to cups of milk)
FUNCTION-
a relation of such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)
DOMAIN-
the set of values of the independent variable for which a function is defined(EXAMPLE: number of cookies)
RANGE-
the set of values of the dependent variable for which a function is defined(EXAMPLE: cups of milk)
INDEPENDENT VARIABLE-
the variable we change in order to measure our output(EXAMPLE: number of cookies)
DEPENDENT VARIABLE-
the variable that changes based on the value that is chosen for the input (EXAMPLE: cups of milk)
DISCRETE VARIABLES-
Variables that only represent incremental values
CONTINUOUS VARIABLES-
Variables that represent all numbers along an interval
SPECIAL CASE-
If all the variables are possible, the domain and range could be "All real numbers"
REPRESENTING DOMAIN AND RANGE:
Discrete Variables: Use set notation!
Ex: {(2,0,1)}
*Domain and Range for discrete variables should be in numerical or alphabetical order!
Continuous Variables: Use interval Notation!
The 5 Different Representations of Relations
- Mapping Diagrams
-Graphs
-Tables
-Ordered Pairs
-Equations
HELPFUL WEBSITES
http://www.micron.com/k12/math/algebra
http://www.analyzemath.com/function/applications.html
http://www.thefutureschannel.com/algebra_real_world.php
http://kanistechnologies.net/index.html
ALL OF THESE ^ HELP IDENTIFY REAL WORLD PROBLEMS
http://springerlink.com/content/450v86667m6660h3/ this website is a written explination about functional relationships
http://www.youtube.com/watch?v=5cK86VKoBPw and here is a video explaining how to find functional relationships
BIG IDEAS
FIVE DIFFERENT REPRESENTATIONS OF MAPPING
the five different representations of mapping are mapping diagrams, tables, ordered pairs, graphs and equasions
WHAT IS A FUNCTION?
a special relation where each input only has one output. No values of the domain can repeat. "The output is a function of the input"
DISCRETE VARIABLES
variables that only represent incremental values EXAMPLE: number of people, states
CONTINUOUS VARIABLES
variables that represent all numbers(fractions and decimals) along an interval EXAMPLE: time, money
REPRESENT DOMAIN AND RANGE
DISCRETE- variables use set notation {-2,0,1} *domain and range for discrete variables should be in numerical or alphabetical order
CONTINUOUS-variables use sinterval notation 0<x<12
SPECIAL CASE
If all values are possible, the domain or range could be "all real numbers"
R=all real numbers
REAL WORLD PROBLEMS
The amount of people in a house depends on the amount of bedrooms.
The amount of flowers in a 4ft by 4ft square depends of the size of the flowers.