# Vertical and Horizontal Asymptotes

• Mar 16th 2009, 05:53 PM
bearhug
Vertical and Horizontal Asymptotes
for the function
$\displaystyle f(x) = \frac {x+5} {2x-4}$
find the vertical and horizontal asymptotes

I know what an asymptote is but I'm not sure how I'm suppose to find it....any help is appreciated!
• Mar 16th 2009, 06:21 PM
Quote:

Originally Posted by bearhug
for the function
$\displaystyle f(x) = \frac {x+5} {2x-4}$
find the vertical and horizontal asymptotes

I know what an asymptote is but I'm not sure how I'm suppose to find it....any help is appreciated!

$\displaystyle y = \frac {x+5} {2x-4}$

we can see that 2x-4=0 , ie x=2 makes the function undefined . Thus , it's a vertical asymtote .

Horizontal aymtotes occur when $\displaystyle y=\lim_{x\rightarrow\infty}f(x)$ is finite .

$\displaystyle y=\lim_{x\rightarrow\infty}\frac{\frac{x}{x}+\frac {5}{x}}{\frac{2x}{x}-\frac{4}{x}}$

y=?? will be the horizontal asymtote
• Mar 16th 2009, 07:01 PM
bearhug
y=0.5?
• Mar 16th 2009, 07:14 PM