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Date Created: 02/09/15
Math 106 Section 6 Notes January 232015 Section 12 Continued 0 To determine if a graph is a function or not it has to pass the VLT Vertical Line Test 0 During testing to see if a problem is symmetric wrt the origin and if there are negative values you can divide by negative one It is still not symmetric wrt the origin An Even Function fx has the property that fx fX o Symmetric wrt the yaxis An Odd Function fx has the property that fx fX o Symmetric wrt the xaxis Determine whether the relation represents y as a function of x 0 You want to solve for y for determining the relation 0 When you square root a relation it results in having a positive and negative value in the solution Therefore it is NOTa function Solving an Equation using a graph Steps to follow 0 Write equation where it is set equal to zero 0 De ne the other side that is not zero as a function 0 Graph the function 0 Then identify the xinterceptsthere graph crosses x axis 0 If you mess up during plotting the points label a couple of the points 0 To get exact valuesljuse graphing utility on desmoscom january 26 2015 Section 13 Linear Functions Linear Function 0 fxmxbm does not 0 Constant Function 0 fxb horizontal lines Note Vertical lines are never a function because it does not pass the VLT Vertical Line Test Slope constant of proportionality for the different in the outputs over the difference in the inputs 0 M is positive then it has a steep slope o M is negative then it has a more level slope o M close to 0 linear function has a slope close to zero Note the greater 39m is the greater sope that the line has Note for a linear function the difference quotient is always constant Linear Function Forms Equations 0 Ymxbj slopeintercept form m byintercept0b o Yylmxx1 pointslope form mslope x1yl a point on graph Functions 0 Fxmxb slopeintercept form 0 Fxmxhk transformation form msope hk any point on graph Hint If the line on the graph is going up left right the slope will always be positive If the line on a graph is going up rightleft the slope will always be negative Parallel Lines vs Perpendicular Lines Parallel Lines two linear functions will have the same slope Perpendicular Lines two distinct linear functions intersect at 90 degree angles Note for nding another perpendicular to another one then you would use the negative reciprocal january 28 2015 Section 13 Continued Rate of Change of fx M change in output over the change in input Average Rate of Change 0 Deltatriangle represents delta x change in x 0 Formula fxdelta xfx all over delta x Note secant line passes through any 2 points on a graph Section 14 Combinations of Functions Sum fgXfXgx Difference fgXfxgx Note pay attention in these particular situationslj you may have negative integers in either fx or gx Multiplication fgXfxgx Note FOIL method is required in this section Division fgxfxgx Note gx CANNOT equal zero January 302015 14 Continued Note You CANNOTdivide by zero for any reason Properties of all real numbers 0 ABO ifand only ifA0 or 30 0 ABO if AO and B DOES NOT0 Note B CANNOT be equal to zero because you CANNOT divide by a zero Domain of fcomposition g x 0 Values of x in domain of gx such that gx is in domain of fx February 22015 Review for Exam 1 o It will cover sections 1114 Determining if the relations are functions or not 0 We are looking for inputs and outputs that are all unique to one another o If you have the same input but differentunique outputs than it will N0Tbe a function because all of the outputs are linked to one particular inputs The Difference Quotient This is one of the formulas and procedures that I will need to know for the exam Natural Domain 0 Different type of functions have different natural domains 0 Linear amp Quadratic in nity in nity oSquare Root 5 in nityl lthis is an example 0 Rational Functions All real numbers EXCEPTwhere dx0 Note Some you will have to use union intervals in nitzl 0 U0 in nity Vertical Line Test VLT Use the VLT to determine if the graph is a function Symmetry wrt the vaxis 0 Determine if mg is in the graph Symmetry wrt the XaXis 0 Determine if Xv2 is on the graph Symmetry wrt the origin 0 Determine if Xv2 is on the graph m Function 0 FXfX 0dd Function 0 FX fX Note if you are able to distribute a negative out of the function it is considered odd NO VIEWING WINDOW QUESTIONS WILL BE ON EXAM Determining if an equation is a function Note if you are square rooting an equation you have to be sure to include both the negative and the positive values February 4 2015 Exam Review Continued Transformation Form 0 Fxmxhk Note h k is a point on the graph and m is the slope NaturaI Domain 0 X1x2 in nity 2U2 in nity Note For the particular problem listed above is demonstrating that the domain has to equal zero that is why 2 is in the nal solution Note pay attention in square root problems in nding the natural domam
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