R.5 Nonlinear functions + Models
R.5 Nonlinear functions + 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 Monday September 21, 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 46 views. For similar materials see QUANTITATIVE METHODS FOR BUSINESS II in Statistics at Temple University.
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Date Created: 09/21/15
R5 Lecture Notes NonLinear Functions 1 Quadratic function F xa x2bxc This graphs a parabola Ushaped graph with a vertex To find the vertex use this formula X 22 61 The opposite of b over 2a What is a vertex it is the highest or lowest point on parabola forms a vertical line of symmetry Conditions of quadratic function 1 a gt 0 positive number graph opens 2 a lt 0 negative number graph opens down 3 a O the equation creates a straight line Solving quadratic equations for x 1 set equation to zero 2 factor equation 3 set each factor to zero 4 solve forx 2 Quadratic formula if factoring doesn t work x bZ CI 2what goes where remember in the quadratic function F xa x2bxc a b and c are all coefficients that get plugged into the quadratic formula ONLY IF FACTORING DOES NOT WORK solve for x 3 Polynomials General form fx anx2 an1x 1 a2x2 a1x looks crazy a coefficients or real numbers xn just x to any exponent What is a degree of a polynomial this is just the value of the highest power 2x3 4x2 x 1 what is the degree of the function 2x3 is the value with the highest exponent so the degree of the function is 3 degree is iust the biggest exoonent Special Cases 1 Quadratic a hx4x2x1 2 Linear a hx X 1 3 Power Function a hx 2x3 DOMAIN OF ANY POLYNOMIAL IS THE REAL LINE 4 Rational Functions rational functions are ratios of two polynomials example y fx hx y 3x2 4x 2x 10 domain excludes any value that would cause the denominator to be zero Inverse Functions y kx k has a degree of O x has a degree of 1 inverse function is NOT defined when x 0 domain ooOUOoo Absolute Value Function y M Domain all real numbers SduareRoot Function Fx X domain xx 2 O 0 00 Rational and Radical Exponents m X DDmnltlltZ gtCI x Z rational form radical form how n the root of x m is the exponent of x going from rational to radical pull n in front of square root sign XAm stays under radical going from radical to rational reverse steps pull X out of the root exponent of X m goes over the root of X n for X A mn IF EXPONENT IS NEGATIVE lT BECOMES A FRACTION 1 mn X mn Application Supply and Demand Demand function the quantity that consumers demand is inversely proportional to the price a decreasing function of price as price goes T demand goes i as price goes i demand goes T Supplv function the quantity that suppliers are willing to produce is propportional to the price an increasing function of price as price goes T supply goes T as price goes i supply goes i Equilibrium Point the point where supply and demand functions cross this is a price point Units are notation the equilibrium point is often denoted as Xe qe Example For supply and demand functions below find the equilibrium point DX 5 X SX X 7 FIRST if you plot demand function you nd that DX O at X 5 Domain of the function XO s X s 5 SECOND we set Demand Supply 5 X X 7 square both sides to get rid of the square root 5 X2 X 72 5 X2 X 7 foil out 5 X2 X21OX25X7 subtract 7 X2 10X 18 X subtract X X211X180 factor X9X2O set each factor to O and solve X 9 X 2 Since X 9 is not in the domain XO s X s 5 the only answer left is X 2 Substitute 2 in for Domain function OR Supply function DX5X DX52 DX3 You get 2 3 as the Equilibrium point
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