
	Where results make sense

Topic: Inverse graph

Related Topics

Interval graph

List of graph theory topics

Sturmgewehr 44

Civilization

Robert Merton

Feudal system

Shang Dynasty

La Paz, Bolivia

In the News (Tue 29 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Inverse Sine and Cosine Functions
		Inverse Function: A function that is derived from a given function by interchanging the two variables.
		To find the inverse of a function, simply interchange the variables when the symbols are abstract, then solve for the new variable in terms of the other.
		Sketch the graphs of the following functions and using the line test described above; decide whether or not their inverses will be functions as well.
	snow.prohosting.com /dandes/Worksheet.htm (401 words)

	PlanetMath: Schützenberger graph
		In what follows, the argument for inverse semigroups and inverse monoids is exactly the same, so we concentrate on the last one.
		Schützenberger graphs play in combinatorial inverse semigroups theory the role that Cayley graphs play in combinatorial group theory.
		This is version 31 of Schützenberger graph, born on 2006-08-20, modified 2006-09-26.
	planetmath.org /encyclopedia/SchutzenbergerGraph.html (168 words)

	Inverse Functions
		To prove that g is the inverse of f we must show that this is true for any value of x in the domain of f.
		Note that the reflected graph does not pass the vertical line test, so it is not the graph of a function.
		The graph of f is a line with slope 3, so it passes the horizontal line test and does have an inverse.
	www.uncwil.edu /courses/mat111hb/functions/inverse/inverse.html (1179 words)

	The Effects of Distance on Count
		This decrease in intensity is proportional to the square of the distance between the source and the detecting device.
		On regular graph paper, plot a graph of the natural log of counts vs. natural log of distance from the source.
		According to the inverse square law, when the distance is doubled from 8 cm to 16 cm, the reading should decrease to 1/4 its initial reading.
	facweb.stvincent.edu /l2l/tmcnulty/Inverse_Lab.htm (711 words)

	GREEAT Science
		Linear graphs are straight lines, such as this graph used to find the density of a rock: The graphs of linear functions are said to have direct relationships.
		Inverse graphs are characterized by a "downhill slope" appearance because they represent relationships that make one thing larger as another thing gets smaller.
		Inverse-r-squared graphs refer to an important category of phenomena such as the strength of the force of gravity, the brightness of light, and other effects, which obey a relationship which is inverse at the same time it is quadratic.
	homepage.mac.com /astronomyteacher/dvhs/grapheq.html (6849 words)

	Inverse functions - Topics in precalculus
		Clearly, dividing by 5 is the inverse of multiplying by 5.
		Let A be a point on the graph of f(x) whose coordinates are (x, y), and which is a distance d from the origin C; AC makes an angle θ with the x-axis; triangle ABC is right angled.
		The graph of g(x) is the graph of the inverse of f(x).
	www.themathpage.com /aPreCalc/inverse-functions.htm (685 words)

	Question Corner -- How To Graph The Inverse Of A Function
		It is actually easier to graph the inverse of a function than it is to solve for it.
		These are the same as the points on the graph of f but with the order of the coordinates interchanged: instead of plotting (x,f(x)) for various numerical values of x, we plot (f(y),y) for various numerical values of y (which is the same thing as plotting (f(x),x) for various numerical values of x).
		Thus the graph which we constructed in this method is not really the graph of a function, since the value of the inverse of f(x) is not well defined at 4 (it could either be 2 or -2).
	www.math.toronto.edu /mathnet/questionCorner/inversegraph.html (453 words)

	Checkpoint - Course 2, Unit 4 (Site not responding. Last check: 2007-10-09)
		We say that time varies inversely with speed, because the time is given by the equation t = d/s, where d is the fixed distance.
		Inverse variation: An inverse variation graph does not cross the axes, the axes are asymptotes.
		Typically, students will graph the relation then focus on a particular point by drawing a horizontal line at the specified value of y, and look for intersection points.
	www.wmich.edu /cpmp/parentsupport/checkpoints/c2u4.html (1200 words)

	Inverse Kinematics on the Java 3D(tm) Scene Graph
		The scene graph is the emergent standard hierarchcal data structure for computer modeling of three dimensional worlds, but kinematic models of machines or mechanisms that have external constraints or constraints that span interior nodes do not sit comfortably on its open-branched tree topology.
		Inverse kinematics solvers have long been fixtures in computational modeling with particular activity in robotics, in human figure animation, and in proprietary CAD and machine design software.
		This paper describes a general approach to solving inverse kinematics on the Java 3D™ scene graph and illustrates the approach using a particular example from classical mechanics with a focus on methods suitable for high fidelity simulation of continuous processes.
	www.brockeng.com /VMech/IK/IKSG.htm (2852 words)

	Exploratorium: Science Snacks: Inverse Square Law
		Put the graph paper at different distances from the bulb, and count how many squares on the graph paper are lit at each distance.
		As the distance from the bulb to the graph paper increases, the same amount of light spreads over a larger and larger area, and the light reaching each square becomes correspondingly less intense.
		When the graph paper is moved 2 inches (5 cm) from the card, four 1/2 inch (1.3 cm) squares will be illuminated on the graph paper.
	www.exploratorium.edu /snacks/inverse_square_law.html (813 words)

	Inverse Functions, Restricted Domains
		Study the graph of a function that is not one-to-one and choose a part of the graph that is one-to-one.
		The graph of the identify function is the straight line that bisects the first and third quadrants and passes through the origin.
		Since an inverse function is a kind of "UNDO" function, the composition of a function with its inverse is the identify function.
	www.sosmath.com /algebra/invfunc/fnc4.html (699 words)

	Inverses
		A useful test to decide from the graph if a function is one to one is the horizontal line test, which is comparable to the vertical line test for functions.
		Suppose that f is a one to one function with inverse g and that (a,b) is a point on the graph of y = f(x).
		Consequently the graph of y=g(x) is the reflection of the graph of y=f(x) across the line y=x.
	www.math.csusb.edu /math110/src/composition/Inverses.html (671 words)

	Math B - Definition of Inverse Function
		For all one-to-one functions, the inverse function is the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function.
		The graph of an inverse is the reflection of the original graph over the identity line y = x.
		by restricting the graph in such a manner, you guarantee the existence of an inverse function for a portion of the graph.
	regentsprep.org /Regents/mathb/7a3/inverselesson.htm (518 words)

	Cycle graph (algebra) - Wikipedia, the free encyclopedia
		In group theory, a sub-field of abstract algebra, a group cycle graph illustrates the various cycles of a group and is particularly useful in visualizing the structure of small finite groups.
		In a cycle graph, the cycle is represented as a series of polygons, with the vertices representing the group elements, and the connecting lines indicating that all elements in that polygon are members of the same cycle.
		Two distinct groups may have cycle graphs that have the same structure, and can only be distinguished by the product table, or by labeling the elements in the graph in terms of the groups basic elements.
	en.wikipedia.org /wiki/Cycle_graph_(algebra) (766 words)

	1.7 - Inverse Functions
		The inverse of a function differs from the function in that all the x-coordinates and y-coordinates have been switched.
		That is, if (4,6) is a point on the graph of the function, then (6,4) is a point on the graph of the inverse function.
		Since all the x-coordinates and y-coordinates are switched when finding the inverse, saying that the inverse must pass a vertical line test is the same as saying the original function must pass a horizontal line test.
	www.richland.edu /james/lecture/m116/functions/inverses.html (1178 words)

	Using the Graphing Calculator with Inverse Functions
		Use the calculator to quickly determine if the inverse of your graph is a function.
		produces the graph of the identity function, y = x, your algebraic inverse answer is correct.
		If your algebraic answer is correct, the bubble animation will follow the inverse graph drawn by the calculator.
	www.mathbits.com /MathBits/TISection/Algebra2/inverse.htm (243 words)

	Inverse function of a given graph
		The first graph does not represent the graph of a function because this graph does not pass the horizontal line test.
		The first graph represents a function but it is not one-to-one.
		The second graph passes the horizontal line test and if two points were selected there ordered pairs do not have the same second components.
	www.chesapeake.edu /khennayake/MAT113/2.7WeeklyQuestionSolution.htm (206 words)

	ON INVERSE FUNCTIONS:INTRODUCTION
		Many students in high school and in college have a difficult time with the concept of inverse functions: what they are, when they exist, how they are used, how to calculate them, how to graph them, and how to interpret their findings.
		If you were to graph the rule, all the points on the graph would consists of pairs of numbers such as (number of hours worked, salary for hours worked).
		For example, if the point (5 hours, $50 salary) is located on the graph of the first function, you would know that the point ($50 salary, 5 hours) would be located on the graph of the inverse function.
	www.sosmath.com /algebra/invfunc/fnc1.html (1370 words)

	Inverse function - Wikipedia, the free encyclopedia
		In mathematics, an inverse function is in simple terms a function which "does the reverse" of a given function.
		If f is a real-valued function, then for f to have a valid inverse, it must pass the horizontal line test, that is a horizontal line y = k placed on the graph of f must pass through f exactly once for all real k.
		Because the range of a left inverse is not restricted, we can adjoin to the domain of this injection an element "undefined", which we then assign to every element of the codomain which is not in the range.
	en.wikipedia.org /wiki/Inverse_function (857 words)

	Inverse Activity
		I expect students to know that the inverse of 2/3 is 3/2, but I want to make sure they understand that this is because when you multiply 2/3 by its inverse, 3/2, you get 1, the multiplicative identity.
		This activity is meant to remind them what an inverse is using an operation with which they are very familiar.
		See that the inverse of an unrestricted parabolic function is not a function.
	www.tcnj.edu /~golazes2/inverse_activity.htm (614 words)

	unit05-sect02-les01-lessond (Site not responding. Last check: 2007-10-09)
		So one of these expressions is the inverse for the function to the right of the axis of symmetry and the other is for the function to the left of the axis of symmetry.
		Clearly from the graph it is the positive radical part we want because (-5, 0) is on the inverse graph, but (-5, -2) is not.
		Note: Generally the positive radical part gives the inverse of the function restricted to the right of the axis of symmetry and the negative radical part gives the inverse restricted to the left of the axis of symmetry.
	www.cdli.ca /courses/math3103/unit05/section01/lesson04/3-lesson-d.htm (278 words)

	Inverse Variation
		This worksheet involves graphing various 1st degree inverse equations and analyzing the effects of changing the values of k.
		Students will graph several inverse variation equations with various constants of variation and examine the effects on the graphs of changing k, and the effects on y of changing x.
		Students are asked to graph data given, calculate the equations which model the data and explain in words each of the equations.
	www.schools.pinellas.k12.fl.us /educators/tec/mincheym/Index.html (385 words)

	Trigonometric and Inverse Trigonometric Function Gallery
		A demo that provides a visual development of the sine and cosine functions and their graphs by 'wrapping' around a circle is available at mathdemos.gcsu.edu.
		At http://www.univie.ac.at/future.media/moe/galerie/wfun/wfun.html under the heading Function 2 are applets and recognition puzzles for graphs of sine and cosine.
		This mathlet illustrates the relationship between the graphs of the natural (radian measure) sine and cosine curves and the vertical and horizontal coordinates of points on the unit circle.
	mathdemos.gcsu.edu /mathdemos/family_of_functions/trig_gallery.html (495 words)

	SparkNotes: Variation: Inverse Variation
		The statement "y varies inversely as x means that when x increases, y decreases by the same factor.
		Unlike the graph of direct variation, the graph of inverse variation is not linear.
		To calculate the constant of variation from a graph of inverse variation, simply pick a point and multiply its two coordinates.
	www.sparknotes.com /math/algebra1/variation/section2.rhtml (357 words)

	FCPS Instructional Services
		Graphing utilities, especially graphing calculators, are integral to the course.
		Sketch graphs with transformations (vertical and horizontal shift, reflection, stretching, and shrinking).
		The student will graph inverse trigonometric functions and identify their domain and range.
	www.fcps.k12.va.us /DIS/pos/math/precalculush316036.htm (2749 words)

	Solving Problems with Proportions
		If it is a strictly inverse proportion, then plotting the intensity vs the reciprocal of distance will yield a straight line graph.
		In this example of an "unknown" proportion, we found that the dependent variable was proportional to the inverse square of the control variable.
		In terms of radioactivity, the decrease in exposure drops as the inverse square of the distance.
	homepage.mac.com /cbakken/proportions/unknown.html (1086 words)

	1.7: Inverse Functions
		In verifying inverse problems, you are given 2 functions, f and g.
		If you graph a function and it's inverse, there will be a reflection about the line y = x.
		This is a new kind of reflection, but it's the came concept as reflection on the x and y axis.
	www.msu.edu /~osstutor/17_s_103.htm (306 words)

	Inverse Functions
		An inverse is the operation that takes you back to where you started. The inverse of multiplication is division, adding and subtracting, square and square root, etc.
		Notice, that this inverse make sense. The original problem had adding by two and the inverse is subtracting two. The original function had multiplying by five and the inverse has division by five.
		If the graph of a function y = f(x) is such that no horizontal line intersects the graph in more than one point, then f has an inverse function.
	home.alltel.net /okrebs/page45.html (381 words)

	Functions - Inverse Functions
		The inverse function of 3x - 4 is (x+4)/3.
		To test if the example above are inverse of each other, do the inverse function test.
		If the graph of the function f is known then the graph of f
	library.thinkquest.org /10030/7invrfun.htm (91 words)

	04brya~1.htm Data Analysis in Algebra II
		These lessons use sets of data which lead to linear, quadratic, inverse variation, and exponential functions, and can be used throughout the course as students acquire knowledge of the particular type of function.
		These two lines may seem a bit different to the students, but graphing them along with the original data should convince them that the method is fairly good (and great, when you do not have a quadratic regression key!).
		Return to the graph and trace to a point which is to the left of the chosen point.
	www.woodrow.org /teachers/mi/1993/04brya.html (3576 words)

	Arrhenius Kinetics Data Analysis
		Initially, a graph displaying rate versus temperature was constructed (Graph 1), and it exhibited an exponential function in which the rate increased drastically with increasing temperature.
		Even though this graph demonstrates a straight line between the two variables, it does not completely illustrate the relationship noted by Arrhenius.
		The resultant graph provides a straight line relationship applicable to all sets of data involving reaction rates at specific temperatures.
	www.sas.upenn.edu /~higginsa/ArrheniusKineticsDataAnalysis.html (481 words)

Try your search on: Qwika (all wikis)