Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 1 Homework, Page 196 Determine whether the function is a power function, given that c, g, k, and π are constants. For those that are power functions, state the power and constant of variation. 1. The function is a power function of power 5 and constant of variation negative one-half.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 2 Homework, Page 196 Determine whether the function is a power function, given that c, g, k, and π are constants. For those that are power functions, state the power and constant of variation. 5. The function is a power function of power 1 and constant of variation c 2.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 3 Homework, Page 196 Determine whether the function is a monomial function, given that c, g, k, and π are constants. For those that are power functions, state the power and constant of variation. 9. The function is a power function of power 2 and constant of variation g/2.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 4 Homework, Page 196 Determine whether the function is a monomial function, given that l and π are constants. For those that are monomial functions, state the degree and leading coefficient. If not, why not. 13. The function is a monomial function of degree 7 and leading coefficient –6.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 5 Homework, Page 196 Write the statement as a power function equation. Use k for the constant of variation if one is not given. 17.The area A of an equilateral triangle varies directly as the square of the length s of its sides.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 6 Homework, Page 196 Write the statement as a power function equation. Use k for the constant of variation if one is not given. 21.The energy E produced in a nuclear reaction is proportional to the mass m, with the constant of variation being c 2, the square of the speed of light.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 7 Homework, Page 196 Write a sentence that expresses the relationship in the formula, using the language of variation or proportion. 25.n = c/v, where n is the refractive index of a medium, v is the velocity of light in the medium, and c is the constant velocity of light in free space. The refractive index of a medium n varies directly as the velocity of light in free space, and inversely as the velocity of light v in the medium.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 8 Homework, Page 196 State the power and constant of variation for the function, graph it, and analyze it as in Example Power – 1/4 Constant of variation: 1/2 Domain: All nonnegative reals Range: All nonnegative reals Continuous Increasing on [0, ∞) Neither even nor odd

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 9 Homework, Page Cont’d Not symmetric Bounded below Local minimum at the origin No asymptotes End Behavior:

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page 196 Describe how to obtain the graph of the given monomial function from the graph of g (x) = x n with the same power n. State whether f is even or odd. Sketch the graph by hand and support your answer with a grapher. 33. To obtain f from g, vertically stretch g by a factor of 1.5 and reflect about the y-axis.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page 196 Match the equation to one of the curves labeled in the figure. 37.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page 196 Match the equation to one of the curves labeled in the figure. 41.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page 196 State the values of the constants k and a for a function f (x) = kx a. Describe the portion of the curve that lies in quadrant I or IV, Determine whether f is even, odd, or undefined for x < 0. Describe the rest of the curve, if any. Graph the function to see whether it matches the description. 45. The portion of the curve in Quadrant IV has the general shape of a parabola. The function is even, the rest of the graph in Quadrant III mirroring the Quadrant IV portion.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page 196 Data are given for y as a power function of x. Write an equation for the power function, and state its power and constant of variation. 49. x y …

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page Diamonds have an extremely high refraction index of n = 2.42 on average over the range of visible light. Determine the speed of light through a diamond.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page The data in the table show the intensity of light from a 100-W light bulb at varying distances. Distance (m)Intensity (W/m 2 )

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page a. Draw a scatter plot of the data. b. Find the power regression model. Is the power close the theoretical value of –2? The power is close to the theoretical –2.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page c. Superimpose the regression curve on the scatter plot. d. Use the regression model to predict the light intensity at 1.7 and 3.4 m.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page Let. Which of the following statements is true? a.b. c.d. e.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 2.3 Polynomial Functions of Higher Degree with Modeling

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide What you’ll learn about Graphs of Polynomial Functions End Behavior of Polynomial Functions Zeros of Polynomial Functions Intermediate Value Theorem Modeling … and why These topics are important in modeling and can be used to provide approximations to more complicated functions, as you will see if you study calculus.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide The Vocabulary of Polynomials

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Graphing Transformations of Monomial Functions

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Cubic Functions

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Quartic Function

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Local Extrema and Zeros of Polynomial Functions A polynomial function of degree n has at most n – 1 local extrema and at most n zeros.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Leading Term Test for Polynomial End Behavior

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Leading Term Test for Polynomial End Behavior

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Applying Polynomial Theory

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Finding the Zeros of a Polynomial Function

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Multiplicity of a Zero of a Polynomial Function

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Zeroes of Odd and Even Multiplicity If a polynomial function f has a real zero c of odd multiplicity, then the graph crosses the x- axis at (c, 0) and the value of f changes sign at x = c. If a polynomial function f has a real zero c of even multiplicity, then the graph does not cross the x-axis at (c, 0) and the value of f does not change sign at x = c.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Sketching the Graph of a Factored Polynomial

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Intermediate Value Theorem If a and b are real numbers with a < b and if f is continuous on the interval [a,b], then f takes on every value between f (a) and f (b). Therefore, if y 0 is between f (a) and f (b), then y 0 = f (c) for some number c in [a,b]. If f (a) and f (b) have opposite signs, then f (c) = 0 for some number c in [a, b].

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Another Box Problem Squares of width x are cut from each corner of a 10-cm by 25- cm sheet of cardboard. The resulting tabs are then folded up to form a box with no top. Determine all the values of x that will result in the box having a volume of, at most, 175 cm 3.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework Review Section 2.3 Page 209, Exercises: 1 – 65 (EOO)