I am looking for a book, which has different many different types of functions and their graphs (like, Weierstrass function, Takagi function).
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
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)
Classical Surveys of Curve Sketching
R. Howard Duncan, Practical Curve Tracing with Chapters on Differentiation and Integration (1910)
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)
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.