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Writing f(x) format of equations

  1. Dec 3, 2007 #1
    1. The problem statement, all variables and given/known data

    How do you write the following in f(x) form? x =1; {3<y<6}
    and (x – 3)2 + (y – 9)2 = .25

    2. Relevant equations

    3. The attempt at a solution

    I had to use these equations in a project that I am graphing and I must also include the f(x) form and I am lost. Can you please help? My project is due tomorrow? I have 6 other equations to put in the f(x) format, but I figured if I could get help on these two I should be able to figure out the others.
  2. jcsd
  3. Dec 3, 2007 #2
    Writing it in f(x) form is (for the sake of simplicity) essentially solving for y (i.e. isolating y so that it is on one side of the '=' sign and everything else that DOES NOT CONTAIN y is on the other side of the '=' sign. For example:

    [tex](x - 3)2 + (y - 9)2 = .25 \implies y = \frac{.25-(x-3)2}{2} + 9
    \implies f(x) = \frac{.25-(x-3)2}{2} + 9 [/tex]

    Generally speaking, one can only obtain the form "[tex]f(x) = \dotsm[/tex]" if the graph is a function (passes the vertical line test). The problem with your first example: [tex] x=1; \{ 3 < y < 6\}[/tex] is that the graph is not a function (it's a vertical line segment).
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