Rational Functions - Revision history

Lila at 19:23, 21 October 2021

2021-10-21T19:23:55Z

Lila: /* Resources */

2021-10-21T19:23:10Z

Resources

Lila: /* Examples */

2021-10-04T18:30:36Z

Examples

Lila: /* Examples */

2021-10-04T18:30:04Z

Examples

Lila: /* Examples */

2021-10-04T18:28:03Z

Examples

Lila: /* Examples */

2021-10-04T18:26:46Z

Examples

Lila: /* ExamplesThis section was cited from en:wikipedia Rational functionoldid=591840157 */

2021-10-04T18:24:56Z

ExamplesThis section was cited from en:wikipedia Rational functionoldid=591840157

Lila at 18:24, 4 October 2021

2021-10-04T18:24:26Z

Lila at 15:30, 15 September 2021

2021-09-15T15:30:59Z

Johnraymond.yanez: Added Links to materials

2020-08-17T14:21:58Z

Added Links to materials

New page

* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Rational_Functions/MAT1053_M4.2Rational_Functions.pdf Rational Functions], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Rational_Functions/MAT1053_M4.2Rational_FunctionsGN.pdf Guided Notes]

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-Rational function is "any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials"<ref name="wiki">This section was cited from en:wikipedia [https://en.wikipedia.org/wiki/Rational_function Rational function]oldid=591840157</ref>.
+Rational function is "any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials".
-==Definition<ref>This sentence was cited from en:wikipedia [https://en.wikipedia.org/wiki/Rational_function Rational function]oldid=591840157</ref>==
+==Definition==
 A function <math>f(x)</math> is called a rational function if and only if it can be written in the form

← Older revision		Revision as of 19:23, 21 October 2021
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	* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Rational_Functions/MAT1053_M4.2Rational_Functions.pdf Rational Functions], Book Chapter		* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Rational_Functions/MAT1053_M4.2Rational_Functions.pdf Rational Functions], Book Chapter
	* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Rational_Functions/MAT1053_M4.2Rational_FunctionsGN.pdf Guided Notes]		* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Rational_Functions/MAT1053_M4.2Rational_FunctionsGN.pdf Guided Notes]
		+
		+	== Licensing ==
		+	Content obtained and/or adapted from:
		+	* [https://en.wikibooks.org/wiki/Intermediate_level_Mathematics/Rational_functions Rational Functions, Wikibooks: Intermediate Level Mathematics] under a CC BY-SA license

@@ Line 12: / Line 12: @@
 ==Examples==
-[[File:RationalDegree3.svg|<math>y = \frac{x^3-2x}{2(x^2-5)}</math>]]
+[[File:RationalDegree3.svg|thumb|<math>y = \frac{x^3-2x}{2(x^2-5)}</math>]]
-[[File:RationalDegree2byXedi.svg|<math>y = \frac{x^2-3x-2}{x^2-4}</math>]]
+[[File:RationalDegree2byXedi.svg|thumb|<math>y = \frac{x^2-3x-2}{x^2-4}</math>]]
 The rational function <math>f(x) = \frac{x^3-2x}{2(x^2-5)}</math> is not defined at <math>x^2=5 \Leftrightarrow x=\pm \sqrt{5}</math>. It is asymptotic to <math>\frac{x}{2}</math> as ''x'' approaches infinity.

@@ Line 12: / Line 12: @@
 ==Examples==
-[[RationalDegree3.svg|<math>y = \frac{x^3-2x}{2(x^2-5)}</math>]]
+[[File:RationalDegree3.svg|<math>y = \frac{x^3-2x}{2(x^2-5)}</math>]]
-[[RationalDegree2byXedi.svg|<math>y = \frac{x^2-3x-2}{x^2-4}</math>]]
+[[File:RationalDegree2byXedi.svg|<math>y = \frac{x^2-3x-2}{x^2-4}</math>]]
 The rational function <math>f(x) = \frac{x^3-2x}{2(x^2-5)}</math> is not defined at <math>x^2=5 \Leftrightarrow x=\pm \sqrt{5}</math>. It is asymptotic to <math>\frac{x}{2}</math> as ''x'' approaches infinity.

@@ Line 12: / Line 12: @@
 ==Examples==
-{{image
+[[RationalDegree3.svg|<math>y = \frac{x^3-2x}{2(x^2-5)}</math>]]
- | header = Examples of rational functions
+[[RationalDegree2byXedi.svg|<math>y = \frac{x^2-3x-2}{x^2-4}</math>]]
 The rational function <math>f(x) = \frac{x^3-2x}{2(x^2-5)}</math> is not defined at <math>x^2=5 \Leftrightarrow x=\pm \sqrt{5}</math>. It is asymptotic to <math>\frac{x}{2}</math> as ''x'' approaches infinity.

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 which may have a larger domain than <math> f(x)</math>, and is equal to <math> f(x)</math> on the domain of <math> f(x).</math> It is a common usage to identify <math> f(x)</math> and <math> f_1(x)</math>, that is to extend "by continuity" the domain of <math> f(x)</math> to that of <math> f_1(x).</math> Indeed, one can define a rational fraction as an equivalence class of fractions of polynomials, where two fractions ''A''(''x'')/''B''(''x'') and ''C''(''x'')/''D''(''x'') are considered equivalent if ''A''(''x'')''D''(''x'')=''B''(''x'')''C''(''x''). In this case <math>\frac{P(x)}{Q(x)}</math> is equivalent to <math>\frac{P_1(x)}{Q_1(x)}</math>.
-==Examples<ref name="wiki">This section was cited from en:wikipedia [https://en.wikipedia.org/wiki/Rational_function Rational function]oldid=591840157</ref>==
+==Examples==
 {{multiple image
   | header = Examples of rational functions

@@ Line 1: / Line 1: @@
 ==Resources==
 * [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Rational_Functions/MAT1053_M4.2Rational_Functions.pdf Rational Functions], Book Chapter
 * [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Rational_Functions/MAT1053_M4.2Rational_FunctionsGN.pdf Guided Notes]

← Older revision		Revision as of 15:30, 15 September 2021
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		+	==Resources==
	* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Rational_Functions/MAT1053_M4.2Rational_Functions.pdf Rational Functions], Book Chapter		* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Rational_Functions/MAT1053_M4.2Rational_Functions.pdf Rational Functions], Book Chapter
	* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Rational_Functions/MAT1053_M4.2Rational_FunctionsGN.pdf Guided Notes]		* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Rational_Functions/MAT1053_M4.2Rational_FunctionsGN.pdf Guided Notes]