1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Range of a function

  1. Oct 7, 2007 #1

    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.

  2. jcsd
  3. Oct 7, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook