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. Sums, Differences, Products, and Quotients Difference Quotients Composition of Functions and Decomposing a Function Algebra of Functions Graphs, Functions, and Models > Algebra of Functions Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra?campaign_content=book_196_section_20&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=dir ect&utm_source=boundless

5. Adding and subtracting equations involves grouping like terms and carrying out basic arithmetic. Multiplying and dividing monomials applies to both like and unalike terms. Multiplying binomials and trinomials follows the FOIL method. Sums, Differences, Products, and Quotients Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/graphs-functions-and-models-2/algebra-of-functions-20/sums-differences- products-and-quotients-112- 5845?campaign_content=book_196_section_20&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess FOIL Method Diagram View on Boundless.com Graphs, Functions, and Models > Algebra of Functions

6. Two points on a graph may give different results when plugged into a function. The difference between two distinct points is known as their Delta (Δ) P, as is the difference in their function result. The function difference between two point values divided by the point difference is known as the difference quotient. The difference quotient is essentially the average slope of a function between two points. In calculus, the difference quotient is used to calculate the derivative when the difference between the two points is infinitesimally small. Difference Quotients Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/graphs-functions-and-models-2/algebra-of-functions-20/difference-quotients- 113- 4642?campaign_content=book_196_section_20&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess View on Boundless.com Graphs, Functions, and Models > Algebra of Functions

7. Functional composition applies one function to the results of another. Functional decomposition resolves a functional relationship into its constituent parts so that the original function can be reconstructed from those parts by function composition. Decomposition of a function into non-interacting components generally permits more economical representations of the function. Composition of Functions and Decomposing a Function Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/graphs-functions-and-models-2/algebra-of-functions-20/composition-of- functions-and-decomposing-a-function-114- 4585?campaign_content=book_196_section_20&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess A Chow-Liu Tree View on Boundless.com Graphs, Functions, and Models > Algebra of Functions

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

9. Key terms binomial A polynomial consisting of two terms, or monomials, separated by addition or subtraction symbols. codomain The target space into which a function maps elements of its domain. It always contains the range of the function, but can be larger than the range if the function is not subjective. derivative The value of this function for a given value of its independent variable. domain The set of all points over which a function is defined. monomial Relative to an algebraic expression consisting of one term. Free to share, print, make copies and changes. Get yours at www.boundless.com Graphs, Functions, and Models

10. A Chow-Liu Tree An example of a sparsely connected dependency structure. Direction of causal flow is upward. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Chow-liu." CC BY-SA http://en.wikipedia.org/wiki/File:Chow-liu.png View on Boundless.comCC BY-SAhttp://en.wikipedia.org/wiki/File:Chow-liu.pngView on Boundless.com Graphs, Functions, and Models

11. General Form of the FOIL Method The general form of the FOIL method using only variables as the potential multipliers. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "FOIL method." GNU FDL http://en.wikipedia.org/wiki/FOIL_method View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/FOIL_methodView on Boundless.com Graphs, Functions, and Models

12. FOIL Method Diagram A color-coded diagram of the FOIL method using both numbers and variables. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "MonkeyFaceFOILRule." CC BY-SA http://en.wikipedia.org/wiki/File:MonkeyFaceFOILRule.JPG View on Boundless.comCC BY-SAhttp://en.wikipedia.org/wiki/File:MonkeyFaceFOILRule.JPGView on Boundless.com Graphs, Functions, and Models

13. Interactive Graph: Difference Quotient Chart The difference quotient can be used to calculate the average slope (here, represented by a straight line) between two points P and Q. Free to share, print, make copies and changes. Get yours at www.boundless.com Boundless. "Interactive Graph: Difference Quotient Chart." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-difference-quotient-chart View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-difference-quotient-chartView on Boundless.com Graphs, Functions, and Models

14. Free to share, print, make copies and changes. Get yours at www.boundless.com Graphs, Functions, and Models What is the result of f(x)=12x4+3x2 divided by g(x)=3x? A) h(x)=4x4+x2 B) h(x)=36x5+9x3 C) h(x)=4x+1 D) h(x)=4x3+x

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/ Graphs, Functions, and Models What is the result of f(x)=12x4+3x2 divided by g(x)=3x? A) h(x)=4x4+x2 B) h(x)=36x5+9x3 C) h(x)=4x+1 D) h(x)=4x3+x

16. Free to share, print, make copies and changes. Get yours at www.boundless.com Graphs, Functions, and Models What is the result when we add f(x)=3x2+2x+1 to g(x)=6x2+4? A) h(x)=9x2+2x+5 B) h(x)=9x2+6x+1 C) h(x)=9x2+5 D) h(x)=6x2+2x+4

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/ Graphs, Functions, and Models What is the result when we add f(x)=3x2+2x+1 to g(x)=6x2+4? A) h(x)=9x2+2x+5 B) h(x)=9x2+6x+1 C) h(x)=9x2+5 D) h(x)=6x2+2x+4

18. Free to share, print, make copies and changes. Get yours at www.boundless.com Graphs, Functions, and Models What is the result when we subtract f(x)=2x-5 from g(x)=x+7? A) h(x)=3x+2 B) h(x)=-x+12 C) h(x)=x+2 D) h(x)=-x+2

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/ Graphs, Functions, and Models What is the result when we subtract f(x)=2x-5 from g(x)=x+7? A) h(x)=3x+2 B) h(x)=-x+12 C) h(x)=x+2 D) h(x)=-x+2

20. Free to share, print, make copies and changes. Get yours at www.boundless.com Graphs, Functions, and Models What is the result when we multiply f(x)=2x-11 and g(x)=6x+1? A) h(x)=12x2-64x-11 B) h(x)=12x2-11 C) h(x)=12x2+68x+11 D) h(x)=8x-10

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/ Graphs, Functions, and Models What is the result when we multiply f(x)=2x-11 and g(x)=6x+1? A) h(x)=12x2-64x-11 B) h(x)=12x2-11 C) h(x)=12x2+68x+11 D) h(x)=8x-10

22. Free to share, print, make copies and changes. Get yours at www.boundless.com Graphs, Functions, and Models Find the difference quotient of the following function: f(x)=2x2+x-2. A) 4x2+x-2 B) 2x+1 C) 4x+1 D) 2x-2

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/ Graphs, Functions, and Models Find the difference quotient of the following function: f(x)=2x2+x-2. A) 4x2+x-2 B) 2x+1 C) 4x+1 D) 2x-2

24. Free to share, print, make copies and changes. Get yours at www.boundless.com Graphs, Functions, and Models Find one decomposition of the function h(x)=(x-3)3+2(x-3)2+1. A) g(x)=(x-3)3 and f(x)=2(x-3)2+1 B) g(x)=x-3 and f(x)=x3+2x2+1 C) g(x)=x and f(x)=x3+x2+1 D) g(x)=(x-3)2+2(x-3)2 and f(x)=1

25. 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/ Graphs, Functions, and Models Find one decomposition of the function h(x)=(x-3)3+2(x-3)2+1. A) g(x)=(x-3)3 and f(x)=2(x-3)2+1 B) g(x)=x-3 and f(x)=x3+2x2+1 C) g(x)=x and f(x)=x3+x2+1 D) g(x)=(x-3)2+2(x-3)2 and f(x)=1

26. Attribution Wikipedia. "Function composition." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Function_compositionCC BY-SA 3.0http://en.wikipedia.org/wiki/Function_composition Wikipedia. "Functional decomposition." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Functional_decompositionCC BY-SA 3.0http://en.wikipedia.org/wiki/Functional_decomposition Wiktionary. "codomain." CC BY-SA 3.0 http://en.wiktionary.org/wiki/codomainCC BY-SA 3.0http://en.wiktionary.org/wiki/codomain Wiktionary. "domain." CC BY-SA 3.0 http://en.wiktionary.org/wiki/domainCC BY-SA 3.0http://en.wiktionary.org/wiki/domain Wikispaces. "BCCalculus - Numerical representations - Difference quotients." CC BY-SA http://bccalculus.wikispaces.com/Numerical+representations+-+Difference+quotientsCC BY-SA http://bccalculus.wikispaces.com/Numerical+representations+-+Difference+quotients Wikipedia. "Difference quotient." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Difference_quotientCC BY-SA 3.0http://en.wikipedia.org/wiki/Difference_quotient Wikipedia. "derivative." CC BY-SA 3.0 http://en.wikipedia.org/wiki/derivativeCC BY-SA 3.0http://en.wikipedia.org/wiki/derivative Connexions. "The algebra of the four basic operations." CC BY 3.0 http://cnx.org/content/m31212/latest/?collection=col11445/latestCC BY 3.0 http://cnx.org/content/m31212/latest/?collection=col11445/latest Wikipedia. "FOIL method." CC BY-SA 3.0 http://en.wikipedia.org/wiki/FOIL_methodCC BY-SA 3.0http://en.wikipedia.org/wiki/FOIL_method Wiktionary. "binomial." CC BY-SA 3.0 http://en.wiktionary.org/wiki/binomialCC BY-SA 3.0http://en.wiktionary.org/wiki/binomial Wiktionary. "monomial." CC BY-SA 3.0 http://en.wiktionary.org/wiki/monomialCC BY-SA 3.0http://en.wiktionary.org/wiki/monomial Free to share, print, make copies and changes. Get yours at www.boundless.com Graphs, Functions, and Models