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Math Help - Fun with Functions

  1. #1
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    Fun with Functions

    construct a function with the x-intercepts only at x=-3 and x=4 such that the limit as x approaches infinity= infinity and the limit as x approaches negative infinity=negative infinity.

    More to come. Please explain how you came to your answer to help me with the questions to follow.

    Thanks,
    moog
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  2. #2
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    Quote Originally Posted by mick1337
    construct a function with the x-intercepts only at x=-3 and x=4 such that the limit as x approaches infinity= infinity and the limit as x approaches negative infinity=negative infinity.

    More to come. Please explain how you came to your answer to help me with the questions to follow.

    Thanks,
    moog
    There can be no continuous function that has these properties, as going to
    \infty as x\rightarrow \infty and -\infty as x\rightarrow -\infty would imply that the function
    crosses the x-axis an odd number of times, which it does not.

    So let:

    <br />
f(x)=\left\{ \begin{array}{cc}(x+3)(x-4),&\mbox{ if } x \ge -10\\<br />
                                         -x, & \mbox{ if } x<-10 \end{array}\right<br />
.

    Here the first part of the function is a quadratic which provides the
    required zero crossings and the required behaviour as x \rightarrow \infty,
    and the second part provides the required behaviour as x \rightarrow -\infty.

    RonL
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  3. #3
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    Well and intercept of the x-axis means that at some point on x y=0. Therfore you do not need to cross the x-axis, but you can just touch it.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by mick1337
    Well and intercept of the x-axis means that at some point on x y=0. Therfore you do not need to cross the x-axis, but you can just touch it.
    Then put a cubic through them:

    f(x)=(x+3)^2(x-4)

    RonL
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  5. #5
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    I realize that this is off topic, but any one who calls himself a 1337 (referring to Mike1337) is a noob haxor
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  6. #6
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    What's a noob haxor?

    ...Rich B.
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  7. #7
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Rich B.
    What's a noob haxor?

    ...Rich B.
    At a guess, something "not nice."

    -Dan

    PS I think he means "n00b h4x0r." There are a variety of definitions:
    http://www.urbandictionary.com/
    Last edited by topsquark; March 8th 2006 at 01:11 PM. Reason: Further information
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  8. #8
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    Quote Originally Posted by Rich B.
    What's a noob haxor?

    ...Rich B.
    A noob haxor is a hacker who thinks he is good. All he can really do is create viruses. Accoriding to the hackers oath: "A hacker never destroys another system." A hacker is supposed to steal infromation, not ruin a computer and make it obvious that there was a hacker attack. There are a lot of hackers who call themselve's 1337 supposed to represent Elite, 4nd th3y t47k l1k3 th15 (and they talk like this). I hate them, I seriously hate them, I will hope will all die out They are noobs (newbies) to the haxing (hacking) methods, this is why I hate them
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