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Math Help - Asymptotes

  1. #1
    HMV
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    Asymptotes

    Can you help me identify any asymptotes that the function g(x)=-(5/3)^x might have?
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  2. #2
    MHF Contributor
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    Quote Originally Posted by HMV View Post
    Can you help me identify any asymptotes that the function g(x)=-(5/3)^x might have?
    have you taken a look at the graph?
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  3. #3
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    hi
    \lim_{x\to +\infty }f(x) = -\infty \Rightarrow \lim_{x\to +\infty }\frac{f(x)}{x} = -\infty
    which means the y-axis is an asymptote.
    and you also have :
    \lim_{x\to -\infty }f(x) = 0 \Rightarrow \lim_{x\to -\infty }\frac{f(x)}{x} = 0
    which means the x-axis is an asymptote.
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Raoh View Post
    hi
    \lim_{x\to -\infty }f(x) = 0 \Rightarrow \lim_{x\to -\infty }\frac{f(x)}{x} = 0
    which means the x-axis is an asymptote.
    Good thought Raoh, but this is not the case. Look at the graph skeeter has posted.

    You can think of a vertical asymptote as any value of the function of x that x is "not allowed" to be. Is there any such value?

    Limits at infinty tell us about y, not x. Think about what you said. By makink the statement \lim_{x\to\infty}f(x), you're assuming that x can be ANY NUMBER!

    P.S. You were correct about the horizotal asymptote.
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  5. #5
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    Thumbs up

    Awesome,thanks a lot,
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