# Talk:Horizontal line test

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## Remove attention tag?

The article is still a stub, but I believe this last set of changes should make the article much more useful for first year calculus students, who are the most likely audience.Brirush (talk) 02:46, 8 November 2012 (UTC)

## Expert attention needed

The term "horizontal line test" is sometimes used in calculus (it is the same idea as Vertical line test). However, this article is written in very general terms and is claimed to be part of set theory, which doesn't make any sense to me, because the bit about graphs and horizontal lines seems to require a real-valued function of a real variable.

Here's an example of its usage in calculus: "The Horizontal Line Test: A function is one-to-one if and only if no horizontal line intersects its graph more than once." (from Stewart, James (2001). Calculus: Concepts and Contexts (2nd ed.). Pacific Grove: Brooks/Cole. p. 65. ISBN 9780534377182.)

Thanks to anyone willing to straighten this out. Possibly it just needs to be re-written to be more like the article Vertical line test, but if there really is some general set-theory importance, I don't want to lose that. --Uncia (talk) 15:22, 5 August 2009 (UTC)

Hi all. I'm totally new to editing the wiki, so I'm a little timid right now. This article needs a rewrite from scratch. It's not difficult subject matter: the "horizontal line tests" are really nothing more than a rephrasing of the definitions of "injective", "surjective", and "bijective", with a visualization for the case of functions R->R. What's the protocol for full rewrites? I can draft something up and put it here if you guys like.
At a minimum, the stuff about continuity has to go. Also, "This is due to the reflective properties of the function over y=x" is probably non-helpful to readers who just want to find out about the horizontal line test. BK Drinkwater (talk) 02:04, 14 September 2009 (UTC)
I agree that the article needs work. Instead of doing an entire rewrite at a single go, it's usually recommended to do a bit at a time. The most urgent need for this article is references so I'd start by trying find some and adding it to the article.--RDBury (talk) 13:39, 15 September 2009 (UTC)
Good call. In that case, I'm getting rid of the sentence about continuity immediately: it manages to be confusing, wrong, and irrelevant all at once. BK Drinkwater (talk) 17:17, 15 September 2009 (UTC)

## Purpose of horizontal line test?

I have trouble following the first line of this article. Is the purpose of the horizontal line test to show injectivity, or surjectivity? Does a function (such as the exponent function) which is injective, but not surjective (nothing mapped to negative real numbers) pass or fail the test? It can't be both... If this is resolved, I would like a third graph, showing an increasing but non-surjective (such as exponential) function, to be labeled "Passes/Fails the test (not surjective)". — Preceding unsigned comment added by 146.142.4.32 (talk) 21:46, 14 February 2012 (UTC)

I have never seen the horizontal line test used to talk about surjectivity or bijectivity. Since everything there was true and potentially useful, I've moved it later in the article and called these "variations" on the test. This makes the definition clearer without losing information. Sarahtheawesome (talk) 23:39, 19 March 2012 (UTC)

## Horizontal line test for quadrilaterals

The horozontal line test is also used to determine if a quadrilateral is convex or not (i.e. it has no angles greater than 180 degrees). It goes as such: "A quadrilateral is convex if and only if any horizontal line intersecting the quadrilateral does so at most two times." It is also true for any line passing through it, but a horizontal line is generally used. For example, a square, rectangle and all of the special quadrilaterals are convex since all lines intersect it twice or once. It's not that hard to find some references for it too. I think that it should be put in the article. 178.135.246.191 (talk) 15:58, 8 March 2013 (UTC)

## potentially merging Horizontal line test and Vertical line test into monotonicity?

The consensus is against merging vertical line test into monotone function. There is no consensus to merge horizontal line test into monotonicity due to insufficient discussion, so there is no prejudice against a new discussion. Cunard (talk) 03:19, 15 August 2016 (UTC)
The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

hi guys,

i know on the surface this proposition may seem unrelated, but wouldn't satisfying properties of strict monotonicity also implicitly satisfy both the vertical and horizontal line tests?

i understand in the case of non-strict monotonicity (i.e. strictly non-decreasing or non-increasing) can introduce a scenario where ${\displaystyle t_{1}, and ${\displaystyle f(x_{t_{1}})=f(x_{t_{2}})}$, thereby violating the horizontal line test, but couldn't we just patch the merged content accordingly?

just spitballin', of course. may help if we merge them into monotonicity under their respective sections, as it may help younger/newer mathematicians see what lies down the road (sorta?).

thanks. 174.3.155.181 (talk) 19:24, 3 July 2016 (UTC)

• Comment Not only young mathematicians, but also readers unfamiliar with this and related territory may be expected to suffer in current circumstances. On looking at these and related articles, it seems to me that the two articles in question are so closely related that to split them up leads to undesirable incoherence. As long as the articles on the two tests are separate, they either must overlap considerably in their text or must refer to each other to a confusing and incoherent degree. Nothing of that kind does the reader any favours. OTOH, creating redirects for each of the terms to mutually articulate sections in the Monotonicity article (or a single coherent section on these tests and generalisations of the principle might be better) should solve all problems. I support the idea of exploring the suggestion, though I am not the right one to do it. JonRichfield (talk) 08:50, 8 July 2016 (UTC)
• Comment I could see potentially integrating the horizontal line test, but how exactly would you integrate the vertical line test into the monotonic function article? Monotonicity seems to be a property of a function, while the vertical line test is about establishing whether or not a given curve is a function. --tronvillain (talk) 21:39, 22 July 2016 (UTC)
• Support merging horizontal line test into monotonicity, as per JonRichfield, provided "horizontal line test" is made as a redirect to the appropriate section of the newly integrated article. SemanticMantis (talk) 16:20, 23 July 2016 (UTC)