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the graph of a function is exactly the same as the function. Also, the co-domain is not determined by the function in this definition. Now, there is the notion of morphism in the category of sets. These are functions (in the set-theoretic sense), but seen as arrows from its domain to its co-domain. As such, the co-domain is part of what the morphism is, as is the domain, and the relation itself. In contexts in which there is interest in studying the properties of functions as morphisms, emphasis is made on making the co-domain part of the definition of the function. For example, if you want to say what it means for a morphism (function!?) to be surjective, you need to look at the morphism, and not just the relation (the set of pairs, the graph alone). Category theory is relatively modern compared to the (set-theoretic) definition of function. It takes some time for language to homogenize. In many introductory books you can even find these two definitions (set-theoretic function and morphism of the category of sets) conflated. They would give the set-theoretic definition as a set of pairs, but then claim, contradictorily that the co-domain is part of the definition of the function. But as of now, both ways of looking at functions are widely used. One only need to make sure in each case, which is being used. Meanwhile, Knowledge would have to also present all the aspects of the current use of the terms 'function', 'graph', 'morphism', etc.
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enforced by the fact that curves have a very long history (more than 2000 years), and that the need of distinguishing between a curve and its graphical representation is very recent (about 100 years). It follows that the disambiguation between the different meanings of a graph is often left to the context. Moreover, using a fully unambiguous wording would often appear as pedantic, which is not really useful.
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1400:." (The bolding there implies that "graph of a relation" is a co-subject of the "graph of a function" article.) "Relation (mathematics)" redirects to "Binary relation", which talks "functional relations" and "non-functional relations" but doesn't show any non-functions, and doesn't mention the word "curve", or state that a "relation" can be a "curve" of any kind.
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as set theory, a function and its graph are essentially the same thing." Which is it? The second statement is sourced, while the first is not, but if the concept of a codomain is part of the definition of a function, the first has to be correct. Also, the section "Is a function more than its graph?" referenced above has disappeared some time in the last decade.
1001:. Mathematically, these have nothing to with the graph of a function, so I think there's a case for removing them. I suppose they might possibly be useful for someone who was confused about the two uses of the word 'graph' in mathematics, but it seems to suggest a link between two areas of mathematics that
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Here, we have a conflict with the common meaning (graphical representation) of "graph", and one of its mathematical meanings. This is rather common, and is generally solved by using, in a mathematical context, a synonymous for the common meaning, here, "plot" instead of "graph". Here, the problem is
891:, is usually a term used for 2d and 3d drawings used in engineering and CAD, and involves things like projections, intersections and possibly more complex curves, all usually in 2D. And as a last point, formally most graph theory people refer to graphical representation of a graph on 2-d plane as a
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The term `graph' should really be restricted to use when referring to actual graphs: nodes and edges. The `graph' of a function as described here is really its plot. This is a common misconception that leads to much confusion, and it irks me that it shows up a lot, even in academia. What would be
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See also
Apostol's Mathematical analysis, which doesn't define graph, but does define (page 35) function, and after that defines mapping, making the distinction clear between these two different concepts. See Bridge's Foundations of Real and Abstract Analysis, in which (page 285) it defines graph of
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Comment: There is a confusion here between the common meaning and the mathematical meaning of "graph", and this is this confusion that I consider as original research: the graph of a function is a mathematical object (a set of pairs of numbers) which is defined independently of any plotting. On the
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and its graphical representation on carthesian plane for n=1 and m=1), even if often chart is actually a graphical representation of the graph (nodes and edges), especially in terms like organizational chart, where you have some directed acyclic graph and nodes are represented as boxes or ovals. In
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The terminology is standard . It is curious that it should be so, but it is. According to a widely adopted approach to the foundations of mathematics, a function, by definition, is a set of ordered pairs satisfying a certain univalence condition. According to that approach, the graph of A is A, and
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The article is now self-contradictory on this point, saying both "Note that although a function is always identified with its graph, they are not the same because it will happen that two functions with different codomain could have the same graph." and "In the modern foundation of mathematics known
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Please, let me know if you know such synonym and if so, where is (and who wrote) the original definition of such a type of "functional dependence"? For my part, I know that E. F. Codd in 1972 applied the concept and used the term as a mean of database design verification/normalization. Dr. Amstrong
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In apparent popular usage (Google hits), one can "plot the function" (6,640,000), "graph the function" (2,710,000), "plot a function" (853,000), or "graph a function" (723,000). "Plot" is most-often the verb. One can "plot the equation" (6,600,000) or "graph the equation" (2,060,000), but it's the
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Definitions in mathematics, and everywhere really, are context dependent. There is the set-theoretic definition, used in foundations of mathematics, and found in pretty much all introductory texts, in which a function is a special type of relation, a set of pairs. In this definition, as you noted,
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I would prefer to merge them with each other but not here. For one thing they do have some properties that are different from the graph of a function (e.g. the application to the definition of convex functions). For another, the graph of a function is a topic of great importance in elementary and
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Please, I have read "We can approximate a function --by mean of several methods-- given a functional dependence of adequate size". It seems to me that "Graph of a function" and "Functional dependence" are very closed concepts and clearly represented by a two columns table with a picture like the
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in his latest video so I came here to see what it said and there is nothing about it here. I'm sure that there is a lot more to it than just that but it makes me think that it would be nice to have a short history section about this subject, or to link to any existing coverage if it is already
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is, or should be, much wider than plotting functions and relations, it includes the plot of any figure such as triangles, and many other things. Also, the concept of "graph of an equation" seems original research, and "graph of a relation" is an ambiguous concept, as a relation on a set
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What is typically used is y vs. x, such that x is horizontal and y is vertical. However, when specifically talking about plotting a function vs. its input, it is more clear and intuitive to plot f(x) vs. x (or f(y) vs. y or whatever), since the variables x and y are just placeholders.
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an underlying generalization thereof, but more like a different concept with a common ancestor. What it has in common is pen, ink, lines, and paper. It SHAREs the name (it is graphical), but "graph theory" isn't primary over number lines and graphing. (Likewise YET ANOTHER THING,
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be merged with each other, but I think they should both be merged here. As far as I can tell from a textbook I looked at briefly, not much can be said about these two notions besides their definition. So I propose to merge them here as derived concepts.
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opposite balance with the indefinite article: "graph an equation" (72,300) or "plot an equation" (19,300). "Plot" is still most-often the verb. But "plot" could mean "make a plot" or "make a graph", and "graph" could mean "make a graph" or "make a plot".
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From the linked
Wolfram Mathworld article, "A graph is sometimes also called a plot." I strongly agree with EmergencyBackupChicken. As far as I can tell, the only purpose this page serves is to perpetuate the misconception that a plot of a function is a
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Article says "In mathematics, the graph of a function f is the collection of all ordered pairs (x,f(x))". The definition given is the definition of a function (so it says that the graph of a function is exactly equal to the function (by set equality)).
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it is hard to see what is accomplished by giving it another name. Nevertheless most mathematicians cheerfully accept the unnecessary word; at the very least it serves as a warning that the same object is about to be viewed from a different angle.
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One can "plot the graph" (4,010,000) or "plot a graph" (481,000); one is much less likely to "graph the plot" (293,000) or "graph a plot" (74,500). So "plot" is what you do - the action, and "graph" is what you made (plotted) - the picture. (See
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contrary, it is not usual in mathematics to call "graph of an equation" the curve of the solutions of a (bivariate) equation; again, this curve is defined independently of any plotting (or graph). The distinction appears clearly in
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A quick look at middle-school texts should confirm which use of "graph" is primary. (Who claims it first? algebra or discrete mathematics?) Bert: "Bring me that graph." Ernie: "What graph? Did you hide it under these
1152:. Secondly, the proposed title suggest wrongly that the article is about plotting of the graphs of graph theory, which is an interesting and difficult problem that deserves its own article. Thirdly, the subject of
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About subjectivity, ..., the domain and the codomain are, normally, a part of the definition of a function. This explain the standard formulation "a function is surjective", without specifying (again) the codomain.
1705:, which maybe 10% of the population learns about, after high school; and maybe 2% are aware of; that thing with the circles, lines, arrows, and labels, but no coordinates; that thing that looks like (I said it!) a
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Maybe this article should be "Graph", after bumping the existing "Graph" to "Graph (disambiguation)". Then this article can cover "graph of a function" and "graph of a relation" without implying that you can't
517:", rather than considering surjection, injection, etc. part of the intrinsic properties of a function, but if this really is the standard formalism then this point should be unambiguous in the article here.
513:, but if codomains are part of the definition of a function then this would seem to be necessary. As a non-mathematician, I'm kind of surprised the standard formulation isn't that "a function is surjective
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axiomatized this kind of dependences in 1974. I try to found the original mathematical concept before its computer application (if really such thing existed before Codd/Amstrong). Thank you.
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Finally, "plot the graph of a function" (250,000) outnumbers "graph the plot of a function" (0), and "plot the graph of an equation" (98,500) outnumbers "graph the plot of an equation" (0).
1823:. In my language (Polish) we do have a separate word for graph of a function (or some other relation) and its graphical representation on 2-d carthesian plane (or even polar cordinates),
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1362:(though the article omits x-y chart)? Or else what is it? An ellipse and a spiral can be polar functions, but an off-center circle has two (or zero) radii per angle, so is not a polar
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Incongruously, "plot of a function" (44,000,000) outnumbers "graph of a function" (13,500,000), but "plot of a function" seems to include "graph of a function" and other results.
1103:– The scope of this article should be widened to cover the graph of a relation, of an equation, etc., which do not have their own articles. At the same time, I am proposing to
1326:, etc. But I don't know what to call them. Knowledge shows many curves, but only seems to call them "curves", never naming the 2-D graphic representation thereof (even though
877:., but image and picture, are essentially synonymous, similar to obraz, portrait, wizerunek and obrazek, last one usually a small picture in a picture frame on a wall).
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This discussion is eternal, and almost unfixable at this point. If talking formally I prefer to refer to 'graph of a function' as a chart (both a set of elements in
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is a person who makes sketches (drawings), usually engineering / mechanical / architectural ones on a paper, and possibly in CAD these days. It plays well with
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a good way to incorporate this information while still allowing people to find what they are looking for after being told the wrong term?
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learns first, circa 7th grade. So why is "Graph" a disambiguation page? THIS should be "Graph"; THAT should be "Graph (disambiguation)".
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Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a
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I was missing these kind of topics. We should also make a list of famous curves if it isn't yet somewhere in
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secondary-school mathematics education and I think adding more advanced concepts such as epigraphs to our article will violate
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graf'. So, I think it is less confusing (we still call portable graphic calculator that makes graphical function charts, as
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That's true if you define functions that way. But I don't think that's a good way to define functions - you really need the
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is confusing: firstly, "graph of a function'" shows clearly that it is about mathematics, which is not the case of
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seems to address this point fairly well. Perhaps this article should be reworded to parallel the discussion there.
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used to refer to the graph of a function (as opposed to a graphical representation of the graph of a function). --
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a mapping, not graph of a function, and clarifies (just like Halmos) that the graph is the same as the function.
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I withdraw my prior renaming suggestion. Maybe this article could or should generalize by being renamed "
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Your objections seem valid except for the equation (it is quite common to display graphs (or plots?) of
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I agree with
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is a relation, but not a function). Is there a better title, which would include these concepts?
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is definitively a things with edges and vertices, its graphical representation usually called a
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973:"Someone else proposed"? I have not found this someone else in the corresponding talk pages. --
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Another Topic
Missing: Graphing Functions. Example: How do you graph the function -3 if x≤-4?
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Nevertheless, as I understand your concern, I have added "For graphical representation see
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continuously plots a parametric function (defined by two functions of time), much like an
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as part of the definition, otherwise how can you tell whether or not the function is
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or "x-y chart with connecting lines" that every spreadsheet program can "chart")? a
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for graphical representation of the function (its 'graph'). For completeness, the
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I also withdraw my previous "proposal" (above). This one might be ready to play:
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I have edited the article for removing some considerations that are
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don't always define functions. x + = 1 "looks like" a unit circle.
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my native language, Polish, we refer to 'graph of a function' as
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I didn't find much else contradicting. A previous version of
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Links to pages about graph theory in the 'See also' section
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Function (mathematics)#Is a function more than its graph?
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x = cos t and y = sin t; same as (x,y) = (cos t, sin t)
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I woke up thinking of this: "The graph of an equation".
502:{\displaystyle \exp ':\mathbb {R} \to \mathbb {R} ^{+}}
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I think the concept embodied in THIS article covers:
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The above discussion is preserved as an archive of a
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it has been "proposed" to move this article to Plot
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1031:by removing these links and expanding the hatnote.
1783:continuously plots one or more functions (of time)
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454:{\displaystyle \exp :\mathbb {R} \to \mathbb {R} }
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1937:Knowledge level-4 vital articles in Mathematics
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1748:." A move or move-request is coming soon... -
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1073:The result of the move request was:
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1142:Strongly oppose to
808:
499:
451:
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101:Mathematics portal
45:content assessment
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766:{x, y | f(x) = y}
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1389:in the intro of
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1216:Curve sketching
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43:on Knowledge's
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1795:vector monitor
1793:; much like a
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1242:requested move
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1105:merge it with
1090:
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1056:requested move
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945:David Eppstein
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879:Unfortunately
861:can also be a
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333:XJamRastafire
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73:High‑priority
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1651:graph of an
1650:
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1642:
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1573:
1565:graph of an
1564:
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1451:graph theory
1405:
1402:
1394:
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1348:scatter plot
1335:
1331:
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1318:, and their
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1199:
1195:
1189:
1185:
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1150:Graph (plot)
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1122:
1104:
1101:Graph (plot)
1091:
1075:no consensus
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999:Graph theory
992:
941:WP:TECHNICAL
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107:
51:WikiProjects
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1667:graph of a
1659:graph of a
1635:graph of a
1624:graph of a
1602:graph of a
1591:graph of a
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1556:graph of a
1548:graph of a
1395:graph of a
1372:yield curve
1298:of various
1252:move review
1066:move review
1003:isn't there
897:81.6.34.246
764:is the set
668:—Preceding
398:? See also
364:following:
344:—Preceding
123:Mathematics
114:mathematics
70:Mathematics
1911:Categories
1849:Mathologer
1827:(close to
1746:map graphs
1576:inequality
1320:I-V curves
1205:Petr Matas
1117:Petr Matas
845:is really
837:is called
770:Metaquanta
396:surjective
319:sin φ ± √(
1883:Functions
1765:Cousins:
1715:. It is "
1682:histogram
1678:bar graph
1561:y = x ÷ x
1495:Equations
1460:Equations
1377:The term
1368:functions
1328:functions
1282:functions
1270:functions
1165:that has
1011:J.Gowers
867:wizerunek
859:wizerunek
847:wizerunek
725:The word
329:many more
39:is rated
1894:D.Lazard
1843:History?
1833:Kreślarz
1725:possibly
1696:everyone
1680:, etc.;
1669:data set
1637:sequence
1626:data set
1615:, or 2-
1567:equation
1558:function
1550:relation
1437:D.Lazard
1397:relation
1379:might be
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1364:function
1346:(like a
1304:ellipses
1286:, but I
1220:D.Lazard
1171:D.Lazard
1123:Relisted
1033:D.Lazard
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959:Txebixev
670:unsigned
584:D.Lazard
557:contribs
545:unsigned
392:codomain
346:unsigned
1829:drawing
1821:drawing
1787:Plotter
1771:Diagram
1708:diagram
1476:Plotter
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1308:spirals
1279:are not
1127:Jenks24
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925:JMP EAX
893:drawing
873:, i.e.
871:picture
863:picture
855:picture
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404:Zundark
255:on the
228:Systems
219:systems
175:Systems
150:on the
41:C-class
1825:wykres
1738:charts
1514:graphs
1332:graphs
1300:curves
1292:graphs
1290:I see
1276:curves
857:, but
821:wykres
331:... --
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1817:Graph
1775:Chart
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1692:Graph
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1296:plots
1288:think
1274:Many
1267:graph
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851:obraz
843:image
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758:graph
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727:graph
576:WP:OR
549:Geoff
519:Geoff
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1898:talk
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247:High
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