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	Even and odd functions - Wikipedia, the free encyclopedia
		Geometrically, an even function is symmetric with respect to the y -axis, meaning that its graph remains unchanged after reflection about the y -axis.
		In general, the sum of an even and odd function is neither even nor odd; e.g.
		The derivative of an even function is odd.
	en.wikipedia.org /wiki/Even_function (492 words)

	[No title]
		Recall from your previous algebra classes that the set of all possible input values for a function is called the domain of the function, and the set of all output values of a function is called the range.
		A function from a set of D to a set R is a rule that assigns an unique element f (x) in R to each element x in D. Remember, for a relation to be a function, it must pass the vertical line test.
		If you are able to graph the function with your graphing calculator, then you can use the fact that an even function is symmetric with respect to the y-axis.
	faculty.eicc.edu /bwood/math150supnotes/preliminary5.htm (1012 words)

	sciforums.com - f(x)=0 Even, Odd, Neither?
		Is f(x)=0 an even function, or an odd function, or is it possible to be both?
		Even functions have a symmetry about the Y axis (f(-x)=f(x)), and odd functions have symmetry about the origin (f(-x)=-f(x)).
		It shares properties, and is a valid function, for both even and odd function characteristics.
	www.sciforums.com /showthread.php?t=10958 (300 words)

	1.4 - Graphs of Functions
		A function is increasing on an open interval if the function rises (positive slope) on the interval as you move from left to right.
		A function is constant on an open interval if the function remains constant (horizontal line segment) on the interval as you move from left to right.
		The greatest integer function is often called the Integer function (or Floor in upper level mathematics), and is abbreviated INT on the calculator.
	www.richland.edu /james/lecture/m116/functions/graphs.html (930 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		Graphically, this means that for an even function, if I were to draw a line segment from $(x_{0},y_{0})$ to $(-x_{0},y_{0})$, the segment would be split into equal lengths by the y axis.
		\begin{figure}[h] \special{psfile=even_fig hscale=50 vscale=50 hoffset=120 voffset=-70} \vspace{2.6cm} \caption{\footnotesize This is the graph of an even function, $f(x)$.
		The graph on the left has the same function with a line from one point on $f(x)$ through the origin to the corresponding point reflected through the origin.
	www.math.utah.edu /~briscoe/spring_1210/correction.ltx (291 words)

	m121prac3key.html
		Consequently, a horizontal translation of any (nonconstant) even function destroys this symmetry and results in a function which is no longer even.
		An even function must be symmetric with respect to the vertical axis.
		Thus, an even function will fail the horizontal line test (unless its graph consists of a single point on the vertical axis).
	www.mtsu.edu /~jhart/m121prac3key.html (593 words)

	29+ Evidences for Macroevolution: Part 2
		Even some professional research biologists have fallen prey to this oversimplification of the vestigial concept (for instance, Scadding 1981, often quoted by anti-evolutionists and discussed in the Citing Scadding (1981) and Misunderstanding Vestigiality FAQ).
		Even though the conclusion may be negative ("structure x has no function"), the detection of biological functionality or lack thereof is based upon positive evidence, not negative evidence.
		In organismic biology, a function is a physical process performed by an organ that is necessary for the successful reproduction of the organism in a specific environment.
	www.talkorigins.org /faqs/comdesc/section2.html (11961 words)

	Handout 2: Odd and Even Functions
		Note that this means that the graph of an even function is symmetric about x = 0 and the graph of an odd function is symmetric about the origin.
		Show that coshx is an even function and sinhx is an odd function.
		Recall that sin is an odd function and cos is an even function.
	www.brunel.ac.uk /~mastsdn/calc2/handout6.html (203 words)

	Math Forum - Ask Dr. Math
		Date: 06/16/98 at 21:50:14 From: Doctor Schwa Subject: Re: Odd and even function constructions An odd function is one where f(-x) = -f(x), and an even function is one where g(-x) = g(x).
		That is, x^(odd power) is an example of an odd function, and x^(even power) is an example of an even function.
		In fact any function h(x) can be written as a sum of an odd and even part, by taking f(x) = (h(x) - h(-x))/2 as the odd part, and g(x) = (h(x) + h(-x))/2 for the even part.
	mathforum.org /library/drmath/view/54565.html (271 words)

	4 Functions (Site not responding. Last check: 2007-11-06)
		A function f is a rule which assigns to each element of a set A a unique element of another set B.
		Since the formula for the inverse function is obtained by finding x in terms of y the graph of the inverse function is obtained from the graph of the function by interchanging the roles of x and y.
		The graph of an even function is symmetrical under reflection in the y -axis.
	www.maths.soton.ac.uk /~rdi/ma155/lectures/node5.html (1190 words)

	Hyperbolic function - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-06)
		In mathematics, the hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.
		The function cosh x is an even function, that is symmetric with respect to the y -axis, and cosh�0�=�1
		Since the exponential function can be defined for any complex argument, we can extend the definitions of the hyperbolic functions also to complex arguments.
	xahlee.org /_p/wiki/Sinh.html (310 words)

	Symmetry Lesson - II
		Because of this correspondence between the symmetry of the graph and the evenness or oddness of the function, "symmetry" in algebra is usually going to apply to the
		It is a function; in fact, it is an even function.
		-axis (that is, for whether the function is even) or about the origin (that is, for whether the function is odd).
	www.purplemath.com /modules/symmetry2.htm (707 words)

	Lab 9 Tail recursion and loops
		In particular, if a function makes a recursive call, but then examines the result and does different things depending on its value, then it may not be possible to make the function tail-recursive.
		Turn the helper function parameters into local variables; their initial values are the same as the initial values for the call to the helper function from the main function.
		The reason for this is that we don't want to evaluate the function bodies once and for all time--rather, we want to check the test expression anew each time that the body is evaluated, and we want to run the body multiple times.
	www.owlnet.rice.edu /~comp210/96spring/Labs/lab09.html (1535 words)

	FS6: Fourier Series for Even and Odd Functions (Site not responding. Last check: 2007-11-06)
		Suppose that f is an even function with period 2L.
		Simplify or evaluate the integrals in Question 2 assuming that f is an even function.
		Write down the form of the Fourier series when f is an even function of period 2L.
	www.math.rpi.edu /Cupples/de/FS6.html (134 words)

	Locks - Encyclopedia - Beckwith's Blades (Site not responding. Last check: 2007-11-06)
		There are numerous modifications to these styles of locks including the addition of buttons to allow operation of a liner lock from the outside of the handle.
		Even so, the locks commonly found in modern blades will safely keep the blade in place under even abusive conditions.
		If the blade lock fails it is most likely due to improper use of the blade as a pry bar or some other function clearly outside of the design parameters of the blade and its lock.
	www.beckwithsblades.com /encyclopedia.cfm?Term=33 (619 words)

	College Algebra Tutorial on Graphs of Functions Part II
		Determine the intervals on which a function is increasing, decreasing or constant by looking at a graph.
		This will be followed by showing you how to tell if a function is even, odd, or neither given either a graph of the function or just its assignment.
		Even the best athletes and musicians had help along the way and lots of practice, practice, practice, to get good at their sport or instrument.
	www.wtamu.edu /academic/anns/mps/math/mathlab/col_algebra/col_alg_tut32_graphfun2.htm (3000 words)

	Math 130, Spring 2001, Lab 2
		A function y=f(x) is said to be an even function if f(-x)=f(x) for each x in the domain of f.
		However, it is interesting that every function can be written as the sum of an even function and an odd function (along as its domain is symmetrical about zero).
		Compute f(x)+g(x) for this pair of functions and show that it is rational by writing it in the form of one polynomial divided by another polynomial.
	math.hws.edu /eck/math130/lab2 (1572 words)

	Visual Calculus - Even and Odd Functions (Site not responding. Last check: 2007-11-06)
		Objectives: In this tutorial, we define what it means for a function to be symmetric with respect to the y-axis and the origin.
		to recognize from the graph of a function whether a function is even, odd or neither; and
		A Quiz on whether a given function is even or odd.
	archives.math.utk.edu /visual.calculus/0/functions.14 (235 words)

	SFSU Engineering 451 - Laboratory #4 - Discrete-time Fourier Transform (Site not responding. Last check: 2007-11-06)
		= X(-w), that is, the magnitude is an even function of w.
		If x[n] is real, show that Xe(w) is a real and even function of w and Xo(w) is a purely imaginary and odd function of w.
		We will assume that the sequences are specified in the manner defined in Laboratory #1, namely as a structure structures with the data array in x.data, and an offset integer in x.offset.
	robotics.eecs.berkeley.edu /~rvidal/engr451/dtft.html (1251 words)

	Lambda (Site not responding. Last check: 2007-11-06)
		A higher order function is a function which is either passed as an argument (to another function) or returned as a value.
		This is because the symbol naming the recursive function is a free variable with respect to the context it occurs in.
		The reason this works is because both functions that had to have mutual knowledge of each other were defined as symbols in a lexical context outside of the context in which the definitions were evaluated.
	www.mactech.com /articles/mactech/Vol.09/09.09/Lambda (1839 words)

	[No title]
		Consider the function EMBED Equation.3 At the point of discontinuity, x = 1, the limit of the function from the left is 1 while the limit from the right is �.
		An example of a function that is not piecewise smooth on the interval [(1, 1] is given by f(x) = x1/3 In fact this function is not piecewise smooth on any interval that includes x = 0 since df/dx = 1/3x-2/3 is (at x = 0.
		An even function is symmetrical with respect to the y-axis while an odd function is symmetrical with respect to the origin.
	www.csupomona.edu /~tknguyen/egr509/Notes/Chapter2-2.doc (1310 words)

	An Introduction to Fourier Theory
		There are functions for which the Fourier transform does not exist; however, most physical functions have a Fourier transform, especially if the transform represents a physical quantity.
		The Fourier transform of an Hermitian function is even.
		If a function or waveform is not periodic, then the Fourier transform of the function will be a continuous function of frequency (Brigham, 4).
	gershwin.ens.fr /vdaniel/Doc-Locale/Cours-Mirrored/Maths-Stuff/fourier (1884 words)

	An application of Discrete Fast Fourier Transform algorithm (Site not responding. Last check: 2007-11-06)
		In addition, the Fourier transform of the complex conjugate of a function f(x) is F*(-s), the reflection of the conjugate of the transform.
		In general, the even part of the Fourier transform of f(x) is the cosine transform of the even part of f(x).
		Since the Fourier transform F(s) is a frequency domain representation of a function f(x), the s characterizes the frequency of the decomposed cosinusoids and sinusoids and is equal to the number of cycles per unit of x.
	www.bridgeport.edu /sed/projects/cs597/Summer_2002/kunhlee (2676 words)

	Is there an odd and even function? (Site not responding. Last check: 2007-11-06)
		If the curve is the graph of a function however the choices are much more limited.
		If (x,y) is on the graph of such a function then (x,-y) is also on the graph since it is symmetric in the x-axis.
		Since the graph is the graph of a function, y = -y.
	mathcentral.uregina.ca /QQ/database/QQ.09.00/saima1.html (141 words)

	Even and Odd Functions
		An even function is also symmetric, but the term symmetric applies also to functions symmetric about a point other than 0.
		Theorem: The product of even functions is even, the product of odd functions is even, and the product of an even times an odd function is odd.
		Since even times even is even, odd times odd is even, and even times odd is odd, we can think of even as
	ccrma-www.stanford.edu /~jos/thms/Even_Odd_Functions.html (179 words)

	Symmetry
		A function symmetrical with respect to the y -axis is called an even function.
		A function that is symmetrical with respect to the origin is called an odd function.
		f (x) is even -- it is symmetrical with respect to the y -axis -- because f (− x) = f (x).
	www.themathpage.com /aPreCalc/symmetry.htm (435 words)

	Math Forum - Ask Dr. Math
		Determining whether a Function is Even or Odd
		Test for evenness: Substitute for (x,y) the pair (-x,y), and solve the two equations simultaneously.
		If the equations are dependent, the function is even.
	mathforum.org /library/drmath/view/54585.html (249 words)

	The function f (x) = xn, Even and Odd Functions
		Even function are symmetrical about the y -axis and odd functions are `skew' symmetrical about the y -axis.
		For example sin(x) is an odd function and cos(x) is an even function (N.B. most functions are neither even nor odd).
		f (x) = f (- x) and the function is Even.
	www.maths.abdn.ac.uk /~igc/tch/ma1002/appl/node33.html (250 words)

	m121prac3.html
		A function f is said to be odd provided f(-x) = - f(x) for all x in the domain of f.
		A function f is said to be even provided f(-x) = f(x) for all x in the domain of f.
		Explain why the function y = 0 is both even and odd.
	frank.mtsu.edu /~jhart/m121prac3.html (392 words)

	NextEven MathArithmetic Function -- Entisoft Tools 2.0 Object Library (Site not responding. Last check: 2007-11-06)
		Function returns Null if vX is Null or cannot be fixed up to a number.
		Note: Similar to calling the Ceiling function with a precision of 2 (two), except that if vX is already an even number, this function returns the next even number.
		Note: Zero is considered an even number, as are all negative numbers divisible by two.
	www.entisoft.com /ESTools/MathArithmetic_NextEven.HTML (118 words)

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