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Transformations of functions

  1. Oct 14, 2005 #1
    hi everyone

    I have trouble recognizing expansions/compressions, and not knowing how draw graphs of recipricol transformations (of functions). can someone explain to me how to "do" them? or recommend a site that has a tutorial about it?

    thanks in advance.
  2. jcsd
  3. Oct 14, 2005 #2


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    It might help to provide a specific example and explain where/how you are having trouble:smile:
  4. Oct 14, 2005 #3
    say f(x) = x^2-5 , how do I graph 1/f(x). Please give an in depth explanation.

    thanks in advance
  5. Oct 14, 2005 #4


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    The easiest way is plot points.
  6. Oct 17, 2005 #5
    can anyone give a solution? not just unfinished sentences.
  7. Oct 17, 2005 #6

    Tom Mattson

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    No, in fact that's the hardest way!

    When graphing rational functions in general, it is best to start by finding the following:

    1.) x-intercepts
    2.) y-intercepts
    3.) Vertical asymptotes
    4.) Horizontal asymptotes
    5.) Slant asymptotes

    Which of these do you know how to find?
  8. Oct 22, 2005 #7
    i really need help, i don't get what you guys are saying.
  9. Oct 23, 2005 #8
    What textbook are you using?
    Does it have paragraphs "Rational Functions and Asymptotes" and
    "Graphs of Rational Functions"?
    g(x) = 1/f(x) is a rational function.
  10. Oct 25, 2005 #9


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    Tom Mattson had it right. You need to look for intercepts and asymptotes. Look at the reciprocal function:


    You need to consider what values of x will cause the function to go to zero, infinity, etc. It's always good to look at limits as x goes to zero and to infinity. You also need to consider what value of x will make the denominator go to zero (meaning what for the value of the function?)
  11. Oct 25, 2005 #10
    what ive atleast been told, ad seems to be a fairly easy way to look at it is to call all the x values in the equation y, then all the y values x ( f(x) for ex would be y.. the changed to x ) first of all, then to solve for y -

    : the first part i allways found confuzing, and useless at best, so in otherwords just switch around the equation to solve for X after you have named f(x) or f(q) or whatever "Y".

    and oh yes- as mentioned above, make sure to disclude answers that will give you nonreal numbers
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