5-1 Polynomial Functions Classify polynomials by describing the degree and end behavior.

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Presentation transcript:

5-1 Polynomial Functions Classify polynomials by describing the degree and end behavior.

Monomials A real number, variable, or product of numbers and variables. A single term o No addition or subtraction Examples: o 18 oZoZ o -4x 2 o 2.5xy

Degree of a monomial Sum of the exponents of its variables o Degree of a constant with no variables is 0 Ex: 5x o Degree 1 6x 3 y 2 o Degree 5 4 o Degree 0

Polynomials

Degree of a Polynomial

Practice

Polynomial Graphs The degree affects the shape of the graph. It also determines the max number of turning points. o Places where the graph changes direction. o There are a max of 1 less turning points than the degree. (quadratics have 1, cubics have 2, quartics have 3, etc.) End behavior tells the direction of the graph to the far left and far right. A function is increasing when y-values increase as x- values increase. A function is decreasing when y-values decrease as x-values increase.

Polynomial Graphs

Practice

Graphing Cubic Functions

Using Differences to Determine Degree Find the degree of the polynomial function that generates the data shown. List y-values vertically. Find the difference between each y-value Do it until the differences are all the same. Values match at 3 rd difference. Degree is 3.

Assignment Odds p.285 #9-39