I am looking for a book, which has different many different types of functions and their graphs (like, Weierstrass function, Takagi function).

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    $\begingroup$ You need to be much more specific about the type of functions you're interested in and about your mathematical level. Right now your question is like asking for a book that discusses different types of machines and their applications (like airplanes, sewing machines, slot machines, electron microscopes, etc.). $\endgroup$ – Dave L Renfro Feb 4 '18 at 11:02
  • $\begingroup$ A book which is a COLLECTION of functions and their respective GRAPHS AT ONE PLACE. About Level , it can be basic to complex. @Dave at last it could be a book which has interesting graphs and not a monotonous style $\endgroup$ – Riya Verma Feb 4 '18 at 12:16
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    $\begingroup$ For your question to be on-topic for this site, it has to be about mathematics education. It is not clear to me what your question is, or if it is about mathematics education. If it is, then please edit it so that the teaching or learning aspect of it becomes clearer. Otherwise, your question will be closed because it is off-topic. $\endgroup$ – Joel Reyes Noche Feb 4 '18 at 13:22
  • $\begingroup$ Try something like "handbook of special functions" or "pathological functions". $\endgroup$ – llllllllllllllllllllllllllllll Feb 4 '18 at 15:14
  • $\begingroup$ Please all of u if u know any name please post. I'm new user please help $\endgroup$ – Riya Verma Feb 4 '18 at 15:20

Here is one I got by Google search. It is Dover (therefore CHEAP).


Also, minor, but look at the free versions of Granville on the web (archive copies). There is a chapter with graphs of cycloids and the like. Little harder than "this is a sin wave", but not as hard as Weirstrass stuff. It is from a different era when people were better at learning from graphs.

I also recommend to look at some basic old school analtical geometry sketching. Look for roots, critical points, asymptotes, etc. Way I learned. Before TI time games. Powerful understanding of relation of formula to shape--more than you get if you let the calculator "grind the pigments" for you. Lot of good videos and class stuff on the net. Old way is still very common.

Here are some videos, but there are lot of written class examples that are good also: https://www.google.com/search?q=curve+sketching+analytic+geometry&client=firefox-b-1-ab&source=lnms&tbm=vid&sa=X&ved=0ahUKEwiFgdfg8ozZAhWGt1kKHfL0ALgQ_AUICygC&biw=1366&bih=654

  • $\begingroup$ Ooh thanku @guest you wrote what I really wanted to ask this only. I WANT TO LEARN functions FROM GRAPHS, so any book kind of this. I'm also searching at "some basic old school analtical geometry sketching including roots, critical points, asymptotes, if any book u know please share $\endgroup$ – Riya Verma Feb 4 '18 at 18:48
  • $\begingroup$ This is the classical approach: youtube.com/watch?v=vOTTuZflAIM $\endgroup$ – guest Feb 4 '18 at 19:06
  • $\begingroup$ Any book which has more examples on it $\endgroup$ – Riya Verma Feb 4 '18 at 19:33
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    $\begingroup$ Check out aproged.pt/biblioteca/ABookofCurvesLockwood.pdf (note that many are relationships, not functions). $\endgroup$ – guest Feb 4 '18 at 19:48
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    $\begingroup$ Take some initiative. Message to Garcia: benning.army.mil/infantry/199th/ocs/content/pdf/… $\endgroup$ – guest Feb 5 '18 at 20:48

Most of the items below were selected based on your comment "I'm also searching at "some basic old school analtical geometry sketching including roots, critical points, asymptotes $[\cdots]$". The Eversole thesis is probably not very well known, the "Weierstrass function" stack exchange question/answer is very limited in scope, and I "stole" the Lockwood book's .pdf file URL from @guest. The others are items I happen to have on my bookshelves that seem especially relevant to classical curve sketching methods (e.g. I have original hardback copies of Gibson/Pinkerton and Osgood/Graustein on my bookshelves). Incidentally, the El-Milick book is quite amazing but appears at present hard to locate. I managed to get a copy (Philip J. Davis’ copy, in fact) back in the early days of internet book buying (2005, I believe), before certain rare but high “general interest” items got snapped up.

Graphs of Exotic Functions

Ruth Eversole, A Collection of Graphs to Accompany Certain Topics in the Study of Function Theory of a Real Variable (1913 Masters thesis)

Who first drew the Weierstrass function?

Classical Surveys of Curve Sketching

R. Howard Duncan, Practical Curve Tracing with Chapters on Differentiation and Integration (1910)

Percival Frost, An Elementary Treatise on Curve Tracing (1918) recently reprinted by Dover Publishers

William Woolsey Johnson, Curve Tracing in Cartesian Coordinates (1884)

J. Dennis Lawrence, A Catalog of Special Plane Curves (1972)

Edward Harrington Lockwood, A Book of Curves (1961)

El-Milick, Éléments d'Algèbre Ornementale (1936)

Especially Comprehensive Textbooks on Analytic Geometry

George Alexander Gibson and Peter Pinkerton, Elements of Analytical Geometry (1911)

William Fogg Osgood and William Caspar Graustein, Plane and Solid Analytic Geometry (1921)

  • $\begingroup$ I feel honored by having you steal something from me. (Not kidding.) $\endgroup$ – guest Mar 10 '18 at 21:21
  • $\begingroup$ @guest: I actually tried to get a copy of Lockwood's book a while back (probably about 10 years ago) and I think I wasn't able to find one online to purchase. It's also not in a nearby University's library (however, 60 miles away, Grinnell College's library has a copy), so I was especially pleased when I saw your link to a freely available digital copy, something that definitely wasn't around when I was looking about 10 years ago. $\endgroup$ – Dave L Renfro Mar 10 '18 at 21:51
  • $\begingroup$ I feel less honored now. (serious.) Thought I came up with something new for you. Still really like your insights. (still serious.) $\endgroup$ – guest Mar 11 '18 at 19:38

The NIST Digital Library of Mathematical Functions has plenty of graphs for most functions.

Another interesting book is

K. B. Oldham,‎ J. Myland,‎ J. Spanier, An Atlas of Functions: With Equator, the Atlas Function Calculator, Springer, 2008.


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