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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 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

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Finding the Domain of a Rational Function Asymptotes Solving Problems with Rational Functions Rational Functions Polynomial and Rational Functions > Rational Functions Free to share, print, make copies and changes. Get yours at ect&utm_source=boundless

A rational function is any function which can be written as the ratio of two polynomial functions. Finding the Domain of a Rational Function Free to share, print, make copies and changes. Get yours at of-a-rational-function ?campaign_content=book_196_section_32&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess View on Boundless.com Polynomial and Rational Functions > Rational Functions

The domain of [Equation 1] is the set of all points x for which the denominator Q(x) is not zero, where one assumes that the fraction is written in its lower degree terms, that is, P and Q have several factors of the positive degree. Polynomial and Rational Functions > Rational Functions Free to share, print, make copies and changes. Get yours at of-a-rational-function ?campaign_content=book_196_section_32&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Equation 1 View on Boundless.com

Domain restrictions can be determined by setting the denominator equal to zero and solving. Free to share, print, make copies and changes. Get yours at of-a-rational-function ?campaign_content=book_196_section_32&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Polynomial and Rational Functions > Rational Functions

An asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity. There are potentially three kinds of asymptotes: horizontal, vertical and oblique asymptotes. A rational function has at most one horizontal asymptote or oblique (slant) asymptote, and possibly many vertical asymptotes. Asymptotes Free to share, print, make copies and changes. Get yours at ?campaign_content=book_196_section_32&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Asymptotes View on Boundless.com Polynomial and Rational Functions > Rational Functions

A rational function is defined as the ratio of two real polynomials with the condition that the polynomial in the denominator is not a zero polynomial. The x-intercepts, also known as zeros of the function or real roots, can be more than one x-intercept. On graphs, x-intercepts are points where a graph intersects the x-axis. Thus, x-intercepts are x-values for which the function has a value of zero. In the case of rational functions, the x-intercepts exist when the numerator is equal to 0. In the case of rational functions, the x-intercepts exist when the numerator is equal to 0. For f(x) = P(x)/Q(x), if P(x) = 0, then f(x) = 0. Solving Problems with Rational Functions Free to share, print, make copies and changes. Get yours at with-rational-functions ?campaign_content=book_196_section_32&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess View on Boundless.com Polynomial and Rational Functions > Rational Functions

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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". denominator The number or expression written below the line in a fraction (thus 2 in ½). domain The set of all points over which a function is defined. numerator The number or expression written above the line in a fraction (thus 1 in ½). oblique Not erect or perpendicular; neither parallel to, nor at right angles from, the base; slanting; inclined. rational function Any function whose value can be expressed as the quotient of two polynomials (except division by zero). Free to share, print, make copies and changes. Get yours at Polynomial and Rational Functions

Interactive Graph: Example of a Rational Function Graph of the rational function. This function has three x-intercepts. Free to share, print, make copies and changes. Get yours at Boundless. "Interactive Graph: Example of a Rational Function." CC BY-SA View on Boundless.comCC BY-SA 3.0https:// View on Boundless.com Polynomial and Rational Functions

Interactive graph: domain of a function Graph of a rational polynomial with equation. The domain of this function is all not equal to +2 or -2. Free to share, print, make copies and changes. Get yours at Boundless. "Boundless." CC BY-SA View on Boundless.comCC BY-SAhttp:// on Boundless.com Polynomial and Rational Functions

Asymptotes The graph of a function with a horizontal, vertical, and oblique asymptote. Free to share, print, make copies and changes. Get yours at Wikipedia. "Asymptote." GNU FDL View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/AsymptoteView on Boundless.com Polynomial and Rational Functions

Attribution Connexions. "Finding the Domain of Simple Rational Functions." CC BY BY 3.0http://cnx.org/content/m13352/latest/ Wikipedia. "Rational function." CC BY-SA BY-SA 3.0http://en.wikipedia.org/wiki/Rational_function Wiktionary. "denominator." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/denominator Wiktionary. "rational function." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/rational+function Wiktionary. "domain." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/domain Wikipedia. "Asymptote." CC BY-SA BY-SA 3.0http://en.wikipedia.org/wiki/Asymptote Wiktionary. "rational function." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/rational+function Wiktionary. "oblique." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/oblique Wiktionary. "asymptote." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/asymptote Connexions. "Rational function." CC BY BY 3.0http://cnx.org/content/m15293/1.10/ Wiktionary. "denominator." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/denominator Wiktionary. "numerator." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/numerator Wiktionary. "rational function." CC BY-SA BY-SA 3.0http://en.wiktionary.org/wiki/rational+function Free to share, print, make copies and changes. Get yours at Polynomial and Rational Functions