Talk:Calculus/Functions
From Wikibooks, the open-content textbooks collection
Contents |
[edit] Kids Section
The final section about "Algebraic manipulation" is really strange , i think the author must assume that the reader of that advanced topic "Calculus" already have this very basic knowledge introduced in that section. i suggest omitting it to make the book more concise and aiming
Would it be worth noting in the Graphing Functions section that graphs are usually of the form y=mx+b, rather than the example which used x=my+b? i.e.:
Functions may be graphed by finding the value of f for various y and plotting the points (y, f(y)) in a Cartesian plane...
2(x+2)/2 = x+2. That's not incorrect. Maybe you meant 2x+2/2 ≠ 2 (x+2)/2 = x+2?
Is a function considered a variable or a rule? f(z) doesn't vary with x; f(x) doesn't vary with z. f(x) may be a variable, but f by itself is a rule or a mapping (or a "machine", as textbooks say). y is a dependent variable because it is understood to vary with x -- y(x) is never used.
What's the plus function doing? + is more common; plus(2,2) is almost never used except in Lisp or something. At least call them add, subtract, divide, multiply instead. Using plus(plus(x,y),z) is not the best way to show grouping because (x+y)+z is more common. Even you use 1/(x+2) at the bottom (instead of divide(1,plus(x,2))). --Geoffrey 15:37 23 Jul 2003 (UTC)
[edit] Points
You have some good points (and one misreading):
I did not write "2(x+2)/2 = x + 2", but rather "2(x+2)/2 = (x+2)/2", and the latter is incorrect.
As for the issue of a function being a variable or rule, I do not make a distinction in these informal pages between the 'rule' (i.e., function), or the result of the rule (i.e., the value of the function). The value of the function is indeed a variable. Making a big deal about distinguishing the two (very different) concepts may only confuse the matter, but an astute reader make take things 'too' literally and notice inconsistancies as you did. The best way of teaching functions is a matter of opinion. Arguably, one should teach functions in a nonstandard way to expose readers to different perspectives or methods, but also arguably, the standard way of teaching functions is standard because of its superiority.
The use of functions plus(x, y) and times(x, y) is to emphasize that the reader has already been doing functions for a long time, and to give the reader something firm to latch onto to relate abstract concepts of arbitrary functions to specific, familar functions. In particular, the composition of functions is confusing, but most people can compose the 'plus' and 'times' functions with ease. Of course, writing out 'plus' and 'times' is somewhat unnecessary.
At User Talk:Eric119 is some more discussion about Calculus/Functions.
If you see anything that needs modification, just go ahead and modify it!
-- IntMan
A graph is a locus of points in the Cartesian plane
I think that the majority of people who can understand the phrase "locus of points in the Cartesian plane" probably already know what a graph is. I think the fact that the majority of us have done maths to a university or higher level is causing us to use language that may be over-complex for our target audience.
--Imran 12:50 27 Jul 2003 (UTC)
- Good point. Also, thanks for the exercises. -- IntMan
Hey, why take out my Example section in basic Calculus??
- Reverted to get rid of the lines, but reverted too far. Sorry. 129.94.6.30 22:17, 11 Feb 2004 (UTC) (User:Dysprosia, logged out)
Ok, thanks :) The lines aren't formatting ppl want? --LWM
- Horizontal rules aren't pretty, and should be used sparingly. Nice exercise, by the way... Dysprosia 20:49, 12 Feb 2004 (UTC)
Could someone please clarify the following?:
- For instance, say that f is the function whose domain contains all positive real numbers that give you a square root of the input.
I had something written, but I retract the question. It was a really dumb question. I really did need to brush up my calculus. GEez
don't know meaning of symbols: I took algebra 2 not too long ago and i have no idea what some of these symbols mean. for example the last function in the table of examples that ends in "Takes an input and uses it as boundary values for an integration." the thing that sort of looks like a sideways 8, and the exact meaning of these [] when in this form: (a,b];[a,b). Any chance of adding the meaning of these? or at least tell me a place where i can find them?--V2os 04:04, 31 July 2005 (UTC)
- I think the last function on the table will be explained later. The sideways 8 stands for infinity. (a,b] is interval notation (first hit on google: http://id.mind.net/~zona/mmts/miscellaneousMath/intervalNotation/intervalNotation.html). And for the Set Notation the funny R means real numbers, and the funny E means the thing on the left is an element of the set on the right (x is an element of the set of real numbers). (disclaimer: I didn't know most of this before today ;) 4.228.240.29
Hrmm... but what happens with:
 |
When x is -3? Isn't the function undefined at that point?
"A function f(x) has an inverse function if and only if f(x) is one-to-one." Is this true? It has to be onto function as well, isn't it?
[edit] ?
it seemse that wiki may have some problems... Look at the section on function manipulation. The formatting seems to have gone all wonky, and I have no idea why. THere is one part where it randomly substitutes a formula from the top of the page, instead of what is written there. If anyone has thoughts on how to fix, please do!
[edit] Problem sets
If this is supposed to be a textbook, where are the problem sets? It can be difficult to just read this and remember it all. I have half a mind to write a problem set. In fact, here's a few problems to get started (I'll leave the finishin' of it to someone more qualified... unless I get fed up):
Find the inverse of the following functions:
- 1. f(x) = 3x2 + 4x
- 2.
Evaluate:
- 3.
where
and- g(x) = 2x2 + 3
216.215.128.84 (talk) 06:57, 15 December 2007 (UTC)
[edit] Length
Anyone else think this page is too long?Tiled (talk) 21:22, 17 November 2009 (UTC)
