# How to find the Key Point and Asymptote

1. Jun 17, 2008

### sollinton

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:

f(x)=2^(x+2)+3

Y-Int=?
Key Point=?
Asymptote=?

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:

f(x)=2^(0+2)+3
f(x)=4+3
f(x)=7

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:

f(x)=2^(0)
f(x)=1

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:

x=2

Your function $$f(x)=2^{x+2}+3$$ has a horizontal asymptote. To find a horizontal asymptote such that $${\lim }\limits_{x \to \infty} f(x)$$ and $${\lim }\limits_{x \to - \infty} f(x)$$ Also, horizontal asymptotes are written as "y="