Find the horizontal and vertical asymptotes of the curve.
y = 4e^x/e^x-6
x=
y= (smaller y - value)
y = (larger y - value)
How do you do this?
I assume you mean:
$\displaystyle y=\frac{4e^x}{e^x-6}$
To find the vertical asymptote(s) solve:
$\displaystyle e^x-6=0$
To find the horizontal asymptote(s) evaluate:
$\displaystyle \lim_{x\to\pm\infty}\frac{4e^x}{e^x-6}$
Vertical asymptotes: $\displaystyle e^x-6=0\Leftrightarrow x=\ln 6$ .
Horizontal asymptotes: $\displaystyle f(x)=\frac{4e^x}{e^x-6}=\dfrac{4}{1-\frac{6}{e^x}}\Rightarrow \begin{Bmatrix} \displaystyle\lim_{x \to{+}\infty}f(x)=4\\\displaystyle\lim_{x \to{-}\infty}f(x)=0\end{matrix}$
Edited: Sorry, I didn't see MarkFL2's post.