EXAMPLE 2 End Behavior of a PolynomialDetermine the end behavior of the polynomialP(x) = -2x* + 5x + 4x – 7

End behaviour of a polynomial decribes the behaviour of the graph of a polynomial at the ends of the…

Answered: EXAMPLE 2 End Behavior of a Polynomial…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.4: Fundamental Theorem Of Algebra And Descartes' Rule Of Signs

Problem 5E

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Similar questions

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Maximize volume An open box is to be constructed from a piece of cardboard 20 inches by 24 inches by cutting a square of length x from each corner and folding up the sides as shown in the figure. a. Write a polynomial function V(x) that expresses the volume of the constructed box as a function of x. b. Use the theory learned about graphing polynomial functions and graph V(x). c. What is the domain of the function as it relates to the application problem? d. Use a graphing calculator to graph the function, and estimate the value of x that gives the maximum volume and then estimate the maximum volume. Round to one decimal place.
Number of Intercepts and Local Extrema How many x-intercepts and how many local extrema does the polynomial P(x)=x34x have? How many x-intercepts and how many local extremadoes the polynomial Q(x)=x3+4x have? If a > 0. bow many x-intercepts and how many local extrema does each Of the polynomials P(x)=x3ax and Q(x)=x3+ax have? Explain your answer.
Using Descartes’ Rule of Signs. we can tell that the polynomial P(x)=x53x4+x2+8x8 has _______________, ____________________positive real zeros and _____________negative real zeros.
Fuel Efficiency The fuel efficiency (in miles per gallon) of a car going at a speed of x miles per hour is given by the polynomial 1150x2+13x . Find the fuel efficiency when x=30 mph.
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Graphing Factored Polynomials Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. P(x)=(x3)(x+2)(3x2)

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EXAMPLE 2 End Behavior of a Polynomial Determine the end behavior of the polynomial P(x) = -2x* + 5x + 4x – 7