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How to find the Key Point and Asymptote

  1. Jun 17, 2008 #1
    1. The problem statement, all variables and given/known data

    I don't particularly need help with any one problem, I just need a refresher on how to find the Key Point and Asymptote of an equation like the following:


    Key Point=?

    2. Relevant equations

    I'm pretty sure I'll only need the original equation f(x)=2^(x+3)+3 and the unmodified equation f(x)=2^(x) lthough I'm not sure if my unmodified version is right.

    3. The attempt at a solution

    From what I remember, to find the Y-Intercept I need to set X equal to zero, and so:


    And so the Y-Intercept would be (0,7)

    I alos remember that finding Key Point has something to do with finding the Y-Intercept without any of the additional modifiers in the equation:


    I'm not even sure I did that right, but assuming I did, I do not know what to do with the answer. I remember I somehow combine it with the Y-Intercept, but I simply cannot remember how.

    For the Asymptote, I believe I simply take the number that modifies the X and set it equal to X:


    Again, I'm not sure about this, so any help would be greatly appreciated
    Last edited: Jun 17, 2008
  2. jcsd
  3. Jun 17, 2008 #2
    Your function [tex]f(x)=2^{x+2}+3 [/tex] has a horizontal asymptote. To find a horizontal asymptote such that [tex]{\lim }\limits_{x \to \infty} f(x)[/tex] and [tex]{\lim }\limits_{x \to - \infty} f(x)[/tex] Also, horizontal asymptotes are written as "y="
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