[Fhsst-authors] Re: hsalgebra.tex and functions

[Sam Halliday]

Clare Johnson wrote:
> thanks - that's the definition of a function I am familiar with. it has to
> pass the "vertical line test" - if you draw a line through the graph
> parallel to the y-axis at any point, it should only cut the graph once. so y
> = sqrt(2-x^2) is a function but x^2 + y^2 = 2 is not.
> 
> I am getting hold of a friend's maths textbook and will look up what the
> definition they use in the syllabus is to be sure.

hmm, it would appear i have gone mad! turns out "function" can mean either...
and no-one seems to have decided upon it yet!

  http://mathworld.wolfram.com/Function.html
  http://mathworld.wolfram.com/MultivaluedFunction.html

i think it might be worth putting in a note or something... in a \footnote{}...
to describe the difference between a "single valued function" and a "multi
valued function"... we can call it the "horizontal line test" instead... and use
the word "function" to mean "single valued function" in our main text.

glad we got that cleared up :-)

also... i noticed a few other small mistakes in hsalgebra.tex... have a look in
the "shifting, reflecting..." section. they are just simple wrong-way-round
mistakes that are easy to make.

thanks for offering to edit this file! it really does need a lot of work :-/

cheers,
Sam
-- 
Free High School Science Texts
  http://savannah.nongnu.org/projects/fhsst
Sam's Homepages
  http://fommil.homeunix.org/~samuel
  http://www.ma.hw.ac.uk/~samuel

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