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Thread: Graph Help

  1. #1
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    Graph Help

    I'm struggling with graphs. Any help appreciated. Thanks

    The figure shows the graphs of
    f(x) = x3 and g(x) = ax3. What can
    you conclude about the value of
    a?

    a.
    a < 1
    b . 1 <
    a < 0
    c . 0 <
    a < 1

    d . 1 <
    a


    Attached Thumbnails Attached Thumbnails Graph Help-picture11.gif  
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    Last edited by ThePerfectHacker; Jun 12th 2007 at 06:58 PM.
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  2. #2
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    We see the following:

    1)$\displaystyle f(x) = g(x) \mbox{ for }x=0$
    2)$\displaystyle f(x) > g(x) \mbox{ for }x>0$
    3)$\displaystyle f(x) < g(x) \mbox{ for }x<0$

    Let us examine #2:

    We know that $\displaystyle f(x) = x^3 \mbox{ and }g(x)=ax^3$
    Thus,
    $\displaystyle x^3 > ax^3 \mbox{ for }x>0$
    $\displaystyle x^3 - ax^3>0$
    $\displaystyle x^3 (1 - a) > 0$
    Since $\displaystyle x>0 \Rightarrow x^3 >0$
    Thus, $\displaystyle (1-a)>0 \Rightarrow a<1$.

    Let us examine #3:
    We know that $\displaystyle x^3 < ax^3 \mbox{ for } x<0$
    $\displaystyle x^3 - ax^3 < 0$
    $\displaystyle x^3 ( 1 - a) < 0$
    This leads to, $\displaystyle a<1$ but we already know that, so we did not gain anything.

    But if we look at $\displaystyle g(x)$ we see that $\displaystyle g(x)>0$ for $\displaystyle x>0$.
    Thus,
    $\displaystyle ax^3 \mbox{ for }x>0$
    Since $\displaystyle x>0$ it tells us that $\displaystyle a>0$.

    Thus,
    $\displaystyle 0<a<1$.
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  3. #3
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    Thanks, And I appreciate the tip about the format to use for pic.
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  4. #4
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    Quote Originally Posted by wvmcanelly@cableone.net View Post
    Thanks, And I appreciate the tip about the format to use for pic.
    Just do not make your picture TOO BIG because then I have to scroll all the way to the right. And I cannot make the resolution smaller because my eyesight is that of Jules Henri Poincare.
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  5. #5
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    Note taken,
    Thanks
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