real Numbers Relations Functions

real Numbers Relations Functions - Transcript

Real Numbers Relations and Functions

Natural Numbers
Counting Numbers
The numbers used for counting That is the numbers 1 2 3 4 etc
Whole Numbers
Nonnegative Integers
The numbers 0 1 2 3 4 5 etc
Integers
or J
Rational Numbers

Note Real numbers that aren t rational are called HYPERLINK http www mathwords com i irrational numbers htm irrational
Real Numbers


Number Line
A HYPERLINK http www mathwords com l line htm line representing the HYPERLINK http www mathwords com s set htm set of all HYPERLINK http www mathwords com r real numbers htm real numbers The number line is typically marked showing HYPERLINK http www mathwords com i integers htm integer values

Coordinate Plane
Cartesian Plane
The HYPERLINK http www mathwords com p plane htm plane formed by a HYPERLINK http www mathwords com h horizontal htm horizontal axis and a HYPERLINK http www mathwords com v vertical htm vertical axis often labeled the x axis and y axis respectively
Coordinates
Ordered Pair
On the HYPERLINK http www mathwords com c coordinate plane htm coordinate plane the pair of numbers giving the location of a HYPERLINK http www mathwords com p point htm point ordered pair
Ordered pair Two numbers written in the form
x y

Scatterplot
A HYPERLINK http www mathwords com g graph of an equation or inequality htm graph of HYPERLINK http www mathwords com p paired data htm paired data in which the data values are plotted as x y HYPERLINK http www mathwords com p point htm points


Relation
A HYPERLINK http www mathwords com s set htm set of HYPERLINK http www mathwords com c coordinates htm ordered pairs
For example 1 2 3 4 1 a 5 r is a relation
So is the set x y y x2 this is the set of all ordered pairs x y for which
y x2
Domain
The HYPERLINK http www mathwords com s set htm set of values of the HYPERLINK http www mathwords com i independent variable htm independent variable s for which a HYPERLINK http www mathwords com f function htm function or HYPERLINK http www mathwords com r relation htm relation is defined Typically this is the set of x values that give rise to real y values
Range
The set of y values of a HYPERLINK http www mathwords com f function htm function or HYPERLINK http www mathwords com r relation htm relation More generally the range is the HYPERLINK http www mathwords com s set htm set of values assumed by a function or relation over all permitted values of the HYPERLINK http www mathwords com i independent variable htm independent variable s
Function
is a function because each number x in the domain has only one possible HYPERLINK http www mathwords com s square root htm square root
is not a function because there are two possible values for any positive value of x
Vertical Line Test
A test use to determine if a HYPERLINK http www mathwords com f function htm relation is a function A relation is a function if there are no HYPERLINK http www mathwords com v vertical htm vertical HYPERLINK http www mathwords com l line htm lines that intersect the HYPERLINK http www mathwords com g graph of an equation or inequality htm graph at more than one HYPERLINK http www mathwords com p point htm point
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