polynomial functions

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Polynomial Functions. 1. Definitions. 2. Degrees. 3. Graphing. Definitions. Polynomial Monomial Sum of monomials Terms Monomials that make up the polynomial Like Terms are terms that can be combined. Degree of Polynomials. Simplify the polynomial Write the terms in descending order - PowerPoint PPT Presentation

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1.4 Fractional Expressions

Polynomial Functions 321DefinitionsDegreesGraphing1DefinitionsPolynomialMonomialSum of monomialsTermsMonomials that make up the polynomialLike Terms are terms that can be combined22Degree of PolynomialsSimplify the polynomialWrite the terms in descending orderThe largest power is the degree of the polynomial

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34A LEADING COEFFICIENT is the coefficient of the term with the highest degree. (must be in order)What is the degree and leading coefficient of 3x5 3x + 2 ?Degree of Polynomials5Degree of PolynomialsPolynomial functions with a degree of 1 are called LINEAR POLYNOMIAL FUNCTIONSPolynomial functions with a degree of 2 are called QUADRATIC POLYNOMIAL FUNCTIONSPolynomial functions with a degree of 3 are called CUBIC POLYNOMIAL FUNCTIONS6Cubic TermTerms of a Polynomial

Quadratic TermLinear TermConstant TermEnd Behavior TypesUp and UpDown and DownDown and UpUp and DownThese are read left to rightDetermined by the leading coefficient & its degree7Up and Up

Down and DownDown and UpUp and DownDetermining End Behavior Typesn is evenn is odda is positivea is negative12

Leading TermUp and UpDown and DownDown and UpUp and DownEND BEHAVIORDegree: Even Leading Coefficient: + f(x) = x2 End Behavior: Up and UpEND BEHAVIORDegree: Even Leading Coefficient: End Behavior: f(x) = -x2 Down and DownEND BEHAVIORDegree: Odd Leading Coefficient: + End Behavior: f(x) = x3 Down and UpEND BEHAVIORDegree: Odd Leading Coefficient: End Behavior: f(x) = -x3 Up and DownTurning PointsNumber of times the graph changes directionDegree of polynomial-1This is the most number of turning points possibleCan have fewer

1717Turning Points (0)f(x) = x + 2LinearFunctionDegree = 11-1=0Turning Points (1)f(x) = x2 + 3x + 2QuadraticFunctionDegree = 22-1=1Turning Points (0 or 2)f(x) = x3 + 4x2 + 2CubicFunctionsDegree = 33-1=2f(x) = x3 Graphing From a FunctionCreate a table of valuesMore is betterUse 0 and at least 2 points to either sidePlot the pointsSketch the graphNo sharp points on the curves2121Finding the Degree From a TableList the points in orderSmallest to largest (based on x-values)Find the difference between y-valuesRepeat until all differences are the sameCount the number of iterations (times you did this)Degree will be the same as the number of iterations2222Finding the Degree From a Tablexy-3-1-2-7-1-305111293-723-6486-2-16104-2-8-14-6-6-6-61st2nd3rd3rd Degree Polynomial23