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4. 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 www.boundless.com www.boundless.com/algebra?campaign_content=book_196_section_32&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=dir ect&utm_source=boundless

5. 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 www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/polynomial-and-rational-functions-4/rational-functions-32/finding-the-domain- of-a-rational-function-157- 5538?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

6. 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 www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/polynomial-and-rational-functions-4/rational-functions-32/finding-the-domain- of-a-rational-function-157- 5538?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

7. 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 www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/polynomial-and-rational-functions-4/rational-functions-32/finding-the-domain- of-a-rational-function-157- 5538?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

8. 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 www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/polynomial-and-rational-functions-4/rational-functions-32/asymptotes-158- 5839?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

9. 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 www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/polynomial-and-rational-functions-4/rational-functions-32/solving-problems- with-rational-functions-159- 5860?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

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

11. 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 www.boundless.com Polynomial and Rational Functions

12. 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 www.boundless.com Boundless. "Interactive Graph: Example of a Rational Function." CC BY-SA 3.0 https://www.boundless.com/image/interactive-graph-example-of-a-rational-function View on Boundless.comCC BY-SA 3.0https://www.boundless.com/image/interactive-graph-example-of-a-rational-function View on Boundless.com Polynomial and Rational Functions

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

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