1. Boundless Lecture Slides Free to share, print, make copies and changes. Get yours at www.boundless.com Available on the Boundless Teaching Platform

2. Using Boundless Presentations The Appendix The appendix is for you to use to add depth and breadth to your lectures. You can simply drag and drop slides from the appendix into the main presentation to make for a richer lecture experience. Free to edit, share, and copy Feel free to edit, share, and make as many copies of the Boundless presentations as you like. We encourage you to take these presentations and make them your own. Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless Teaching Platform Boundless empowers educators to engage their students with affordable, customizable textbooks and intuitive teaching tools. The free Boundless Teaching Platform gives educators the ability to customize textbooks in more than 20 subjects that align to hundreds of popular titles. Get started by using high quality Boundless books, or make switching to our platform easier by building from Boundless content pre-organized to match the assigned textbook. This platform gives educators the tools they need to assign readings and assessments, monitor student activity, and lead their classes with pre-made teaching resources. Get started now at: If you have any questions or problems please email: educators@boundless.com http://boundless.com/teaching-platform

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4. The Leading-Term Test Finding Zeroes of Factored Polynomials Introduction: Polynomial and Rational Functions and Models Polynomial Functions and Models Polynomial and Rational Functions > Polynomial Functions and Models Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra?campaign_content=book_196_section_28&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=dir ect&utm_source=boundless

5. Properties of the leading term of a polynomial reveal whether the function increases or decreases continually as x values approach positive and negative infinity. If n is odd and an is positive, the function declines to the left and inclines to the right. If n is odd and an is negative, the function inclines to the left and declines to the right. If n is even and an is positive, the function inclines both to the left and to the right. If n is even and an is negative, the function declines both to the left and to the right. The Leading-Term Test Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/polynomial-and-rational-functions-4/polynomial-functions-and-models-28/the- leading-term-test-143- 725?campaign_content=book_196_section_28&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss View on Boundless.com Polynomial and Rational Functions > Polynomial Functions and Models

6. A polynomial function may have zero, one, or many zeros. All polynomial functions of positive, odd order have at least one zero, while polynomial functions of positive, even order may not have a zero. Regardless of odd or even, any polynomial of positive order can have a maximum number of zeros equal to its order. Finding Zeroes of Factored Polynomials Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/polynomial-and-rational-functions-4/polynomial-functions-and-models- 28/finding-zeroes-of-factored-polynomials-144- 8064?campaign_content=book_196_section_28&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess View on Boundless.com Polynomial and Rational Functions > Polynomial Functions and Models

7. Researchers will often collect many discrete samples of data, relating two or more variables, without knowing the mathematical relationship between them. Curve fitting is used to create trend lines intended to fill in the points between and beyond collected data points. Polynomial functions are easy to use for modeling but ill-suited to modeling asymptotes and some functional forms, and they can become very inaccurate outside the bounds of the collected data. Rational functions can take on a much greater range of shapes and are more accurate both inside and outside the limits of collected data than polynomial functions. However, rational functions are more difficult to use and can include undesirable asymptotes. Introduction: Polynomial and Rational Functions and Models Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/polynomial-and-rational-functions-4/polynomial-functions-and-models- 28/introduction-polynomial-and-rational-functions-and-models-145- 5880?campaign_content=book_196_section_28&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Curve Fitting View on Boundless.com Polynomial and Rational Functions > Polynomial Functions and Models

8. Free to share, print, make copies and changes. Get yours at www.boundless.com Appendix

9. Key terms asymptote A line that a curve approaches arbitrarily closely, as they go to infinity; the limit of the curve, its tangent "at infinity". Leading coefficient The coefficient of the leading term. Leading term The term in a polynomial in which the independent variable is raised to the highest power. zero Also known as a root, a zero is an x value at which the function of x is equal to 0. Free to share, print, make copies and changes. Get yours at www.boundless.com Polynomial and Rational Functions

10. Interactive Graph: Cubic Function in Factored Form Graph of cubic function in factored form of. Notice that f(x) crosses the x axis at x=-3, x=-1, and x=2. Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Interactive Graph: Cubic Function in Factored Form." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-cubic-function-in-factored- form View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-cubic-function-in-factored- formView on Boundless.com Polynomial and Rational Functions

11. Interactive Graph: Graph of a Cubic Polynomial Graph of a cubic polynomial with the quadratic equation. How does the shape change when you change the a term? When you change the n term? Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Interactive Graph: Graph of a Cubic Polynomial." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-graph-of-a-cubic-polynomial View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-graph-of-a-cubic-polynomialView on Boundless.com Polynomial and Rational Functions

12. Curve Fitting Polynomial curves generated to fit points (black dots) of a sine function: The red line is a first degree polynomial; the green is a second degree; the orange is a third degree; and the blue is a fourth degree. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Curve fitting." CC BY-SA http://en.wikipedia.org/wiki/File:Curve_fitting.jpg View on Boundless.comCC BY-SAhttp://en.wikipedia.org/wiki/File:Curve_fitting.jpgView on Boundless.com Polynomial and Rational Functions

13. Example of a quadratic/linear rational function Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Boundless." CC BY-SA http://www.boundless.com/ View on Boundless.comCC BY-SAhttp://www.boundless.com/View on Boundless.com Polynomial and Rational Functions

14. Free to share, print, make copies and changes. Get yours at www.boundless.com Polynomial and Rational Functions Describe the end behavior of f(x)=3x3-2x2+x-7. A) The function inclines to the left and declines to the right. B) The function inclines both to the left and to the right. C) The function declines both to the left and to the right. D) The function declines to the left and inclines to the right.

15. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Polynomial and Rational Functions Describe the end behavior of f(x)=3x3-2x2+x-7. A) The function inclines to the left and declines to the right. B) The function inclines both to the left and to the right. C) The function declines both to the left and to the right. D) The function declines to the left and inclines to the right.

16. Free to share, print, make copies and changes. Get yours at www.boundless.com Polynomial and Rational Functions Describe the end behavior of f(x)=-x2-5x+3. A) The function declines to the left and inclines to the right. B) The function inclines to the left and declines to the right. C) The function inclines both to the left and to the right. D) The function declines both to the left and to the right.

17. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Polynomial and Rational Functions Describe the end behavior of f(x)=-x2-5x+3. A) The function declines to the left and inclines to the right. B) The function inclines to the left and declines to the right. C) The function inclines both to the left and to the right. D) The function declines both to the left and to the right.

18. Free to share, print, make copies and changes. Get yours at www.boundless.com Polynomial and Rational Functions The graph of f(x)=(x-2)(x+9)(x+5) has zeros at: A) -2, 9, and 5 B) 2, -9, and -5 C) 0 and 90 D) 0 and -90

19. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Polynomial and Rational Functions The graph of f(x)=(x-2)(x+9)(x+5) has zeros at: A) -2, 9, and 5 B) 2, -9, and -5 C) 0 and 90 D) 0 and -90

20. Free to share, print, make copies and changes. Get yours at www.boundless.com Polynomial and Rational Functions Find the zeros of the following function: f(x)=(x+3)2(x-2). A) 3 and -2 B) -3, 3, and -2 C) -3 and 2 D) -3, 3, and 2

21. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Polynomial and Rational Functions Find the zeros of the following function: f(x)=(x+3)2(x-2). A) 3 and -2 B) -3, 3, and -2 C) -3 and 2 D) -3, 3, and 2

22. Free to share, print, make copies and changes. Get yours at www.boundless.com Polynomial and Rational Functions What is one advantage of using rational functions as models rather than polynomial functions? A) All of these answers. B) Rational functions can effectively model asymptotes. C) Rational functions can take on a greater range of shapes. D) Rational functions are more accurate with predictions both inside and outside the range of data.

23. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Polynomial and Rational Functions What is one advantage of using rational functions as models rather than polynomial functions? A) All of these answers. B) Rational functions can effectively model asymptotes. C) Rational functions can take on a greater range of shapes. D) Rational functions are more accurate with predictions both inside and outside the range of data.

24. Attribution Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//algebra/definition/leading-coefficientCC BY-SA 3.0http://www.boundless.com//algebra/definition/leading-coefficient Wikipedia. "Leading term." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Leading%20termCC BY-SA 3.0http://en.wikipedia.org/wiki/Leading%20term Wikipedia. "Coefficient." CC BY-SA 3.0 http://en.wikipedia.org/wiki/CoefficientCC BY-SA 3.0http://en.wikipedia.org/wiki/Coefficient Wiktionary. "asymptote." CC BY-SA 3.0 http://en.wiktionary.org/wiki/asymptoteCC BY-SA 3.0http://en.wiktionary.org/wiki/asymptote Wikipedia. "Polynomial and rational function modeling." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Polynomial_and_rational_function_modelingCC BY-SA 3.0 http://en.wikipedia.org/wiki/Polynomial_and_rational_function_modeling Wikipedia. "Properties of polynomial roots." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Properties_of_polynomial_rootsCC BY-SA 3.0http://en.wikipedia.org/wiki/Properties_of_polynomial_roots Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//algebra/definition/zeroCC BY-SA 3.0http://www.boundless.com//algebra/definition/zero Free to share, print, make copies and changes. Get yours at www.boundless.com Polynomial and Rational Functions