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Math Help - Graphing e graphs

  1. #1
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    Exclamation Graphing e graphs

    Is there a faster way to graph expressions with 'e' in them? Whenever I graph them I have to put in a few x values manually into the expression to see what the graph looks like and then find the turning points

    How do I find the asymptotes for these graphs? I'm having trouble with graphing y=x-e^x - Is the asymptote y=-1?

    The other problem: one of the expressions is y=(e^x)/(x-1)
    I've been taught that to find the asymptotes you divide everything by the highest x power in the denominator and anything when simplified is still over x is marked as a zero (something to do with limits)

    What about (e^x)/x? Is it possible to simplify that?

    Thanks!
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  2. #2
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    Re: Graphing e graphs

    I suppose you need to recognize that the graph y=e^x only has a horizontal asymptote to the left, none to the right. That asymptote being the negative x-axis , i.e. y = 0 as x → -∞ .

    The graph y=e^{-x} is a reflection through the y-axis of y=e^x\,.

    For the cases you mention, it's handy to be able to visualize the resulting graphs for adding/subtracting functions & multiplying/dividing functions.
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  3. #3
    MHF Contributor Siron's Avatar
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    Re: Graphing e graphs

    You're talking about asymptotes, but which asymptotes?
    For example, if you have given: f(x)=\frac{e^x}{x-1}
    H.A:
    - \lim_{x\to +\infty} \frac{e^x}{x-1}, you can use in this case l'Hopitals rule and so you get:
    \lim_{x\to +\infty} e^{x}=+\infty
    - \lim_{x \to -\infty}\frac{e^x}{x-1}=0

    So one H.A, y=0
    ...

    Try to search for the other asymptotes.
    You can't simplify \frac{e^x}{x}
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