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Math Help - functions mappings, domain and range?

  1. #1
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    functions mappings, domain and range?

    hi, how do you find if the mapping of a function is one-one, many-one or many to many?
    for example:

    a) y= tanx
    b) y = y= x^2 - x - 2
    c) y^2 = x + 1

    do i need to sketch the curve or something?


    my second question is i know how to find the range and domain but do you need to ALWAYS sketch a curve for a given function or is there a method that maybe can be done with inspection?

    thanks a lot
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  2. #2
    MHF Contributor
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    Quote Originally Posted by llkkjj24 View Post
    hi, how do you find if the mapping of a function is one-one, many-one or many to many?
    for example:

    a) y= tanx
    b) y = y= x^2 - x - 2
    c) y^2 = x + 1

    do i need to sketch the curve or something?


    my second question is i know how to find the range and domain but do you need to ALWAYS sketch a curve for a given function or is there a method that maybe can be done with inspection?

    thanks a lot
    1-to-1 means that given f(x), if f(a)=f(b) if and only if a=b. That's just saying that any y-value must have only one x-value. If you have two points on the graph like (1,5) and (2,5) then the graph isn't of a one-to-one function. An easy way to test this graphically is to look at all horizontal lines that could intersect the graph. If a horizontal line can touch the graph at two points, it's not one-to-one.

    See here for a better description: Horizontal line test - Wikipedia, the free encyclopedia

    Without using graphs, look for things like even functions, trig expressions that contain an x, absolute value signs, etc. Things like (x)^2 make -x and x the have the same output and graphs that repeat the same path over and over again like sin(x) won't work as well.
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