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Thread: now how do i find the aymptotes?

  1. #1
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    now how do i find the aymptotes?

    $\displaystyle 3^{x+2}-1$

    How do I find the asymptotes of this (vertical, horizontal)?
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  2. #2
    Junior Member
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    let f(x) = 3^x
    this graph has f(x) > 0

    then 3^(x+2) -1

    is a transformation on f(x)
    so:

    f(x+2) - 1

    this is a vertical translation of -1 and a horizontal translation of left 2 units

    we care only about the vertical translation
    now we have f(x) > -1

    so the horizontal asymptote is y = -1
    since the curve approaches -1 when x is large negative
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  3. #3
    Super Member flyingsquirrel's Avatar
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    Hi
    How do I find the asymptotes of this (vertical, horizontal)?
    Vertical asymptotes exist where the function is not defined : at the boundaries of its domain, each time that $\displaystyle \lim_{x\to x_0}f(x)=\pm\infty$, $\displaystyle x=x_0$ is a vertical asymptote for the curve.
    Horizontal ones exist when the function has a limit when $\displaystyle x$ approaches $\displaystyle \pm\infty$. (for example $\displaystyle y=0$ is an horizontal asymptote as $\displaystyle x$ approaches both $\displaystyle -\infty$ and $\displaystyle \infty$ for $\displaystyle x\mapsto\frac{1}{x}$)
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