Great books on curve sketching?

[SecretSnow]

Hi everyone, I'm currently looking for a book on ways to sketch curves, especially for the more unusual kinds of curves, something that teaches things like hyperbolic curves, x^x, sigmoid functions and so on. These are what I have not encountered in my learning very often, so I'm interested to find out more on these. Are there any good books that teaches these curves and the way to draw it? Any book that shows lots of curves like these alone is good too. Thank you guys!

 

[pasmith]

Hi everyone, I'm currently looking for a book on ways to sketch curves, especially for the more unusual kinds of curves, something that teaches things like hyperbolic curves, x^x, sigmoid functions and so on. These are what I have not encountered in my learning very often, so I'm interested to find out more on these. Are there any good books that teaches these curves and the way to draw it? Any book that shows lots of curves like these alone is good too. Thank you guys!

You are unlikely to find such a text¹. There are general principles (which really don't take up more than a page to state) which can be used to obtain a sketch of the graph of a function:
1. What are the domain and range?
2. Where does the graph intersect the coordinate axes?
3. Does the graph have any symmetries (is it an even/odd function or a translation of an even/odd function)?
4. Where are the critical points (if any)?
5. Are there any vertical asymptotes?
6. What does the function do as its argument tends to infinity?

The next step is to compute values of the function for some values of the argument and plot those points, and then connect them with smooth curves bearing in mind the answers to the previous six questions. If plotting more than one curve on the same axes then you also need to pay attention to whether, and if so approximately where, the curves intersect.

¹ I did manage to find a public domain text (Frost, Percival (1918). An Elementary Treatise on Curve Tracing. MacMillan), which from the date predates the universal availability of plotting programs. The author notes that

it would be of some advantage to have read the first section of Newton's Principia, but I hope that questions concerning limits and curvature will be made clear independently of such reading

which suggests that it also predates the universal availability of introductory calculus texts (which ought to explain the basic principles of curve-sketching at some point).