Khanh at 04:07, 14 November 2021

2021-11-14T04:07:16Z

Johnraymond.yanez: Added Links to materials

2020-08-17T14:12:43Z

Added Links to materials

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* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Domain_Range_and_Toolkit_Functions/MAT1053_M1.2Domain_Range_and_Toolkit_Functions.pdf Domain Range and Toolkit Functions], Book Chapter
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Domain_Range_and_Toolkit_Functions/MAT1053_M1.2Domain_Range_and_Toolkit_FunctionsGN.pdf Guided Notes]

← Older revision		Revision as of 04:07, 14 November 2021
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		+	==Definition==
		+	In mathematics, the range of a function may refer to either of two closely related concepts:
		+	* The codomain of the function
		+	* The image of the function
		+	Given two sets X and Y, a binary relation f between X and Y is a (total) function (from X to Y) if for every x in X there is exactly one y in Y such that f relates x to y. The sets X and Y are called domain and codomain of f, respectively. The image of f is then the subset of Y consisting of only those elements y of Y such that there is at least one x in X with f(x) = y.
		+
		+	In algebra, the range (or codomain) of a function is all of the possible outputs of the function. That is, if x is any element of the domain of some function f, then f(x) is in the range of the function f.
		+
		+	Examples:
		+	* Let <math>S</math> be a set of ordered pairs such that <math> S = \{(1,2), (2,3), (4, 7), (13, 9), (-20, 0)\}</math>. The range is the set of all y values of <math>S</math>, so the range is <math>\{0, 2, 3, 7, 9\}</math>.
		+	* The range of <math> g(x) = 1/x </math> is all real numbers EXCEPT for 0. We know this because for all nonzero real numbers M, 1/M is a nonzero number and is in the domain of <math> g(x) </math> (since the domain of this function is all nonzero numbers). So, we know that <math> 1/(1/M) = M </math> is in the range, where M is all nonzero numbers. There is no real number M such that <math> 1/M = 0 </math> though, which is why 0 is not in the range of <math> g(x) </math>.
		+	* The range of <math> h(x) = x^2 + 2 </math> is <math> [2,\inf) </math>. We can see this on the graph of <math> h(x) </math> easily: the lowest point, or vertex, of the parabola is at (0, 2), so 2 is in the range. The parabola extends up to infinity on either side of the vertex, so we know that the range must be all numbers from 2 to infinity.
		+
		+	==Resources==
	* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Domain_Range_and_Toolkit_Functions/MAT1053_M1.2Domain_Range_and_Toolkit_Functions.pdf Domain Range and Toolkit Functions], Book Chapter		* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Domain_Range_and_Toolkit_Functions/MAT1053_M1.2Domain_Range_and_Toolkit_Functions.pdf Domain Range and Toolkit Functions], Book Chapter
	* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Domain_Range_and_Toolkit_Functions/MAT1053_M1.2Domain_Range_and_Toolkit_FunctionsGN.pdf Guided Notes]		* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Domain_Range_and_Toolkit_Functions/MAT1053_M1.2Domain_Range_and_Toolkit_FunctionsGN.pdf Guided Notes]
		+
		+	== Licensing ==
		+	Content obtained and/or adapted from:
		+	* [https://en.wikipedia.org/wiki/Range_of_a_function Range of a function, Wikipedia] under a CC BY-SA license

Range - Revision history

Khanh at 04:07, 14 November 2021

Johnraymond.yanez: Added Links to materials