R.2 Functions and Models
R.2 Functions and Models STAT 1102 - 003
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STAT 1102 - 003
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This 4 page Class Notes was uploaded by Kayla Notetaker on Saturday September 19, 2015. The Class Notes belongs to STAT 1102 - 003 at Temple University taught by Ron Kershner in Fall 2015. Since its upload, it has received 113 views. For similar materials see QUANTITATIVE METHODS FOR BUSINESS II in Statistics at Temple University.
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Date Created: 09/19/15
Chapter R2 Functions and Models Notes What is a function a functions mandates that every value of x is assigned to exactly one value of fx also known as y Example 0 every x value red dotted line has a matching y value green dotted line Y can be written in a number of ways fXgXhXy quotthey all mean the same thing So how do we know if it s a function The vertical line test shows the realness of a function Definition a graph is a function if a vertical line passes through the graph on only one point Domain and Range Functions are graphed by domain and range A domain are the xvalues xaxis and range are the yvalues yaxis Domain contains ALL of the xvalues for which the function in defined OR where the graph appears We can find domains graphically or algebraically VEHIEEI Line Test 3 axle 1 axis this graph is a function because the green line only passes through the graph at one value of x HOWEVER more than one x can match up to the same y value BUT one x cannot match up to more than one y Example more than one x to one y This is still a function because when you draw a vertical line through any x on the graph it F1 4 passes through the graph only g once at any point x3 only goes to y4 If x3 matched with y4 AND y5 it is not a function ill I I I I I I Example This is NOT a function The line passes through the graph more than one time Horizontal Line Test This is the same as the Vertical Line Test but using a Horizontal line If functions pass Horizontal Line Test they are onetoone functions onetoone one x per y value and one y per x value These functions have inverses Example Horizontal line passes through graph once This is a onetoone function IMPORTANT ONE TO ONE FUNCTIONS Fist One to One functions are inverses yzlnfx F Eh y lnr32ii PieceWise Functions These types of functions depend on the portion of the graph they occupy This is limited by their domain which is a set of xvalues Example gx 2x 3 xlt1 x 2 x Z 1 Here the first equation is represented by the green line and the second equation by the blue line In a piecewise function the equations are limited to where they appear on the graph by the domain represented by the inequalities xlt1 and x gt 1
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