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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. Basics of Graphing Polynomial Functions The Intermediate Value Theorem Graphing Polynomial Functions Polynomial and Rational Functions > Graphing Polynomial Functions Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra?campaign_content=book_196_section_29&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=dir ect&utm_source=boundless

5. The graph of the zero polynomial f(x) = 0 is the x-axis. Basics of Graphing Polynomial Functions 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/graphing-polynomial-functions-29/basics- of-graphing-polynomial-functions-146- 5195?campaign_content=book_196_section_29&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess View on Boundless.com Polynomial and Rational Functions > Graphing Polynomial Functions

6. The graph of a degree 1 polynomial (or linear function) [Equation 1], where a1 ≠ 0, is an oblique line with y-intercept a0 and slope a1. Polynomial and Rational Functions > Graphing Polynomial Functions 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/graphing-polynomial-functions-29/basics- of-graphing-polynomial-functions-146- 5195?campaign_content=book_196_section_29&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Equation 1 View on Boundless.com

7. The graph of a degree 2 polynomial [Equation 2], where a2 ≠ 0 is a parabola. Polynomial and Rational Functions > Graphing Polynomial Functions 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/graphing-polynomial-functions-29/basics- of-graphing-polynomial-functions-146- 5195?campaign_content=book_196_section_29&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Equation 2 View on Boundless.com

8. The graph of any polynomial with degree 2 or greater [Equation 3], where an ≠ 0 and n ≥ 2 is a continuous non-linear curve. Polynomial and Rational Functions > Graphing Polynomial Functions 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/graphing-polynomial-functions-29/basics- of-graphing-polynomial-functions-146- 5195?campaign_content=book_196_section_29&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Equation 3 View on Boundless.com

9. Simply stated, the Intermediate Value Theorem points out that: if the plotted route between points A and C is smooth and continuous between point A to point C, you will have to pass through all points "B" on the journey, as long as they are on the plotted route. The Intermediate Value Theorem capitalizes on the completeness of functions of real numbers. Functions containing irrational roots do not meet the requirements of the Intermediate Value Theorem. The Intermediate Value Theorem 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/graphing-polynomial-functions-29/the- intermediate-value-theorem-147- 1092?campaign_content=book_196_section_29&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess The Intermediate Value Theorem View on Boundless.com Polynomial and Rational Functions > Graphing Polynomial Functions

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

11. Key terms continuous Without break, cessation, or interruption; without intervening time. indeterminate not accurately determined or determinable. interval A distance in space. polynomial an expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power, such as a_n x^n + a_{n-1}x^{n-1} +... + a_0 x^0. Importantly, because all exponents are positive, it is impossible to divide by x. term any value (variable or constant) or expression separated from another term by a space or an appropriate character, in an overall expression or table. Free to share, print, make copies and changes. Get yours at www.boundless.com Polynomial and Rational Functions

12. Interactive Graph: Continuous Function A graphed third-order equation where. It meets the requirements of the Intermediate Value Theorem. In what situation would it not meet the requirements for the theorem? Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Interactive Graph: Continuous Function." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-continuous-function View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-continuous-functionView on Boundless.com Polynomial and Rational Functions

13. Interactive Graph: Graphing a Rational Function A graph of a rational function,. A discontinuity occurs when : the function is not defined at $x=-2$. Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Interactive Graph: Graphing a Rational Function." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-graphing-a-rational-function View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-graphing-a-rational-functionView on Boundless.com Polynomial and Rational Functions

14. The Intermediate Value Theorem In plotting a continuous and smooth function between two points, all points on the function between the extremes are described and predicted by the Intermediate Value Theorem. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia. CC BY-SA http://upload.wikimedia.org/wikipedia/commons/c/ce/Intermediatevaluetheorem.png View on Boundless.comCC BY-SAhttp://upload.wikimedia.org/wikipedia/commons/c/ce/Intermediatevaluetheorem.pngView on Boundless.com Polynomial and Rational Functions

15. Interactive Graph: Graph of 6th-Degree Polynomial Graph of a polynomial function of a degree 6, with the equation. Notice how many times the graph crosses the x-axis. Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Interactive Graph: Graph of 6th-Degree Polynomial." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-graph-of-6th-degree- polynomial View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-graph-of-6th-degree- polynomialView on Boundless.com Polynomial and Rational Functions

16. Interactive Graph: Graph of 2nd-Degree Polynomial Graph of a polynomial function of a degree 2, with the equation. Notice how many times the graph crosses the x-axis. Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Interactive Graph: Graph of 2nd-Degree Polynomial." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-graph-of-2nd-degree- polynomial View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-graph-of-2nd-degree- polynomialView on Boundless.com Polynomial and Rational Functions

17. Interactive Graph: Graph of 5th-Degree Polynomial Graph of a polynomial function of a degree 5, with the equation. Notice how many times the graph crosses the x-axis. Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Interactive Graph: Graph of 5th-Degree Polynomial." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-graph-of-4th-degree- polynomial-1b1c258d-599c-41c2-94e6-591c29f3928b View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-graph-of-4th-degree- polynomial-1b1c258d-599c-41c2-94e6-591c29f3928bView on Boundless.com Polynomial and Rational Functions

18. Interactive Graph: Graph of 4th-Degree Polynomial Graph of a polynomial function of a degree 4, with the equation. Notice how many times the graph crosses the x-axis. Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Interactive Graph: Graph of 4th-Degree Polynomial." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-graph-of-4th-degree- polynomial View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-graph-of-4th-degree- polynomialView on Boundless.com Polynomial and Rational Functions

19. Interactive Graph: Graph of 3rd-Degree Polynomial Graph of a polynomial function of a degree 3, with the equation. Notice how many times the graph crosses the x-axis. Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Interactive Graph: Graph of 3rd-Degree Polynomial." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-interactive-graph-graph-of- 3rd-degree-polynomial View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-interactive-graph-graph-of- 3rd-degree-polynomialView on Boundless.com Polynomial and Rational Functions

20. Interactive Graph: Graph of 3rd-Degree Polynomial Graph of a polynomial function of a degree 3, with the equation. Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Interactive Graph: Graph of 3rd-Degree Polynomial." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-graph-of-3rd-degree- polynomial View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-graph-of-3rd-degree- polynomialView on Boundless.com Polynomial and Rational Functions

21. Free to share, print, make copies and changes. Get yours at www.boundless.com Polynomial and Rational Functions Without actually graphing it, what do we know to be true about the following polynomial: f(x)=x2+3x+5? A) It crosses the x-axis two times. B) All of these answers. C) It is continuous. D) It passes the vertical line test.

22. 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 Without actually graphing it, what do we know to be true about the following polynomial: f(x)=x2+3x+5? A) It crosses the x-axis two times. B) All of these answers. C) It is continuous. D) It passes the vertical line test.

23. Free to share, print, make copies and changes. Get yours at www.boundless.com Polynomial and Rational Functions A polynomial graph crosses the x-axis four times. Which of the following polynomials could represent this graph? A) f(x)=3x4-6x5+2x-9 B) f(x)=4x2+4x+4 C) f(x)=x3+4x2-3x4 D) f(x)=2x2+3x3+x

24. 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 A polynomial graph crosses the x-axis four times. Which of the following polynomials could represent this graph? A) f(x)=3x4-6x5+2x-9 B) f(x)=4x2+4x+4 C) f(x)=x3+4x2-3x4 D) f(x)=2x2+3x3+x

25. Free to share, print, make copies and changes. Get yours at www.boundless.com Polynomial and Rational Functions A continuous function: A) has no holes. B) has no asymptotes. C) all of these answers. D) is smooth.

26. 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 A continuous function: A) has no holes. B) has no asymptotes. C) all of these answers. D) is smooth.

27. Free to share, print, make copies and changes. Get yours at www.boundless.com Polynomial and Rational Functions If f(2)=2 and f(10)=25, and f(x) is continuous from 2 to 10, then the intermediate value theorem tells us: A) that somewhere between 2 and 10, f(x) must equal 20. B) that f(5)=16. C) that f(x) crosses the x-axis between 2 and 10. D) that the function is continuous over all x-values.

28. 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 If f(2)=2 and f(10)=25, and f(x) is continuous from 2 to 10, then the intermediate value theorem tells us: A) that somewhere between 2 and 10, f(x) must equal 20. B) that f(5)=16. C) that f(x) crosses the x-axis between 2 and 10. D) that the function is continuous over all x-values.

29. Attribution Wikipedia. "Intermediate value theorem." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Intermediate_value_theoremCC BY-SA 3.0http://en.wikipedia.org/wiki/Intermediate_value_theorem Wikipedia. "Continuous function." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Continuous_functionCC BY-SA 3.0http://en.wikipedia.org/wiki/Continuous_function Wiktionary. "interval." CC BY-SA 3.0 http://en.wiktionary.org/wiki/intervalCC BY-SA 3.0http://en.wiktionary.org/wiki/interval Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//psychology/definition/continuousCC BY-SA 3.0http://www.boundless.com//psychology/definition/continuous Wikipedia. "Polynomial." CC BY-SA 3.0 http://en.wikipedia.org/wiki/PolynomialCC BY-SA 3.0http://en.wikipedia.org/wiki/Polynomial Wiktionary. "term." CC BY-SA 3.0 http://en.wiktionary.org/wiki/termCC BY-SA 3.0http://en.wiktionary.org/wiki/term Wiktionary. "polynomial." CC BY-SA 3.0 http://en.wiktionary.org/wiki/polynomialCC BY-SA 3.0http://en.wiktionary.org/wiki/polynomial Wiktionary. "indeterminate." CC BY-SA 3.0 http://en.wiktionary.org/wiki/indeterminateCC BY-SA 3.0http://en.wiktionary.org/wiki/indeterminate Free to share, print, make copies and changes. Get yours at www.boundless.com Polynomial and Rational Functions