# Talk:Graph of a function

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## Topics missing

I was missing these kind of topics. We should also make a list of famous curves if it isn't yet somewhere in Wikipedia. For instance the Watt's curve in spherical polar coordinates: r2 = b2 - (a sin φ ± √(c2 - a cos2 φ))2 and many more ... --XJamRastafire 19:15 Sep 18, 2002 (UTC)

Another Topic Missing: Graphing Functions. Example: How do you graph the function -3 if x≤-4?

—Preceding unsigned comment added by 99.37.114.196 (talk) 22:42, 19 October 2010 (UTC)

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 following:

```x | y
--+---
5 | 11
2 |  5
1 |  3
```

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 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. [Enrique Villar; mailto:evillarm@capgemini.es]

## Graph of a function equals the function?

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)). 24.84.213.237 07:38, 7 May 2007 (UTC)

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 codomain as part of the definition, otherwise how can you tell whether or not the function is surjective? See also Function (mathematics)#Is a function more than its graph?. --Zundark 08:56, 7 May 2007 (UTC)

## Is it typically y vs x or x vs y?

Is it typically y vs x or x vs y? —Preceding unsigned comment added by 64.180.160.235 (talk) 05:23, 16 January 2009 (UTC)

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. EmergencyBackupChicken (talk) 17:00, 7 May 2009 (UTC)

## Graph vs. Plot?

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 a good way to incorporate this information while still allowing people to find what they are looking for after being told the wrong term? EmergencyBackupChicken (talk) 17:00, 7 May 2009 (UTC)

The word graph is used in both senses in mathematics. I don't think I've ever seen plot used to refer to the graph of a function (as opposed to a graphical representation of the graph of a function). --Zundark (talk) 09:13, 8 May 2009 (UTC)

## Merge epigraph and hypograph

Someone else proposed that Hypograph (mathematics) and Epigraph (mathematics) 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. JMP EAX (talk) 08:27, 1 August 2014 (UTC)

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 secondary-school mathematics education and I think adding more advanced concepts such as epigraphs to our article will violate WP:TECHNICAL. —David Eppstein (talk) 01:47, 3 December 2014 (UTC)
I agree with Eppstein. The notion of epigraph is quite unrelated with what is discussed in this page. --Txebixev (talk) 22:25, 25 January 2015 (UTC)
"Someone else proposed"? I have not found this someone else in the corresponding talk pages. --Txebixev (talk) 22:27, 25 January 2015 (UTC)

In the 'See also' section of this article, there are links to the articles Graph (mathematics) and Graph theory. 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 isn't there.  J.Gowers  19:53, 1 May 2015 (UTC)

Fixed by removing these links and expanding the hatnote. D.Lazard (talk) 20:38, 1 May 2015 (UTC)

## Requested merge and move 14 January 2016

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section.

The result of the move request was: no consensus. Jenks24 (talk) 08:50, 1 February 2016 (UTC)

Graph of a function + Plot (graphics)Graph (plot) – 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 merge it with Plot (graphics), because their scopes are strongly overlapping; note that it has been "proposed" to move this article to Plot. Petr Matas 11:42, 14 January 2016 (UTC) Relisted. Jenks24 (talk) 05:53, 24 January 2016 (UTC)

• Strongly oppose to both move and merge. The move proposed for Graph of a function is confusing: firstly, "graph of a function'" shows clearly that it is about mathematics, which is not the case of Graph (plot). 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 Plot (graphics) 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 S is nothing else than a directed graph that has S as a set of vertices. D.Lazard (talk) 13:16, 14 January 2016 (UTC)
Your objections seem valid except for the equation (it is quite common to display graphs (or plots?) of x2 + y2 = 1 and the like) and the relation (on R; for example, inverse of sin x is a relation, but not a function). Is there a better title, which would include these concepts? Petr Matas 13:55, 14 January 2016 (UTC)
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 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 Curve sketching. "Graph of an equation" is further confusing, as it is not the equation that is graphed, but the curve of the solutions. D.Lazard (talk) 14:46, 14 January 2016 (UTC)

The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.