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Range of a function

  1. Oct 7, 2007 #1
    Hi.

    Could someone please tell me the Core 3 way of finding the range of f(x) = (2x - 3) / (x - 2).

    I have no idea how to draw the graph.

    Any help would be really appreciated.

    Thank you.

    Cathy
     
  2. jcsd
  3. Oct 7, 2007 #2

    arildno

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    Well, you know that x can't be 2, right?

    Now, let "t" denote some arbitrary real number; we are to find out what x must be in order for f to eqal f:
    [tex]t=\frac{2x-3}{x-2}\to(x-2)t=2x-3\to{x}=\frac{2t-3}{t-2}, x\neq{2}[/tex]
    Thus, t=2 is an inadmissible value for the function.

    Note that t=2 is a horizontal ASYMPTOTE for f(x) as x trundles off to either infinity.

    Furthermore, there are no t-value such that [tex]\frac{2t-3}{t-2}=2[/tex], whereupon we have shown that the range of f is all real numbers except 2.
     
    Last edited: Oct 7, 2007
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