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Simple questions abt functions.

  1. Aug 31, 2006 #1
    Is the following correct.

    1. f(x) is a function if for every x value there is exactly one y value. so sin x is a function.

    2. does a 1-1 function mean that the line y = constant cut the graph in exactly one place? therefore sin (x) is not a 1:1 function but is still a function?

    :redface:
     
  2. jcsd
  3. Aug 31, 2006 #2
    Yes that is correct.

    [tex] \\sin x[/tex] is a function that is a many to one function. That is there are multiple x values that give the same value as y or f(x). For example if you sub in [tex]x={\pi}/{2}[/tex] and [tex]x={5\pi}/{2}[/tex] into [tex]y= \\sin x[/tex] you get y=1 in both cases.

    Thus you have a many to one function. There is also a many to many graph which obviously isn't a function due to the vertical line test.
     
    Last edited: Aug 31, 2006
  4. Aug 31, 2006 #3
    Number 2 is not correct. A function (from R to R) is injective if and only if the line y = constant cuts the graph in AT MOST one place.
     
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