1. ## intercepts and asymptotes

Sketch a graph of the given rational function. Identify any intercepts and any asymptotes.

$f(x)=2x+6/x-4$

Vertical Asymptote:
x-4=0
4=x

Horizontal Asymptote:
y=2

x-intercept:
2x+6=0
3=x
(3,0)

y-intercept:
f(0)=2(0)+6/0-4
=3/-2
(0,3/-2)

I don't know if this is right. Now I just don't know where to plot the points. I need help with this. Thank you in advance.

2. Originally Posted by theevilp0ptart
Sketch a graph of the given rational function. Identify any intercepts and any asymptotes.

$f(x)=2x+6/x-4$

Vertical Asymptote:
x-4=0
4=x

Horizontal Asymptote:
y=2

x-intercept:
2x+6=0
3=x
(3,0)

y-intercept:
f(0)=2(0)+6/0-4
=3/-2
(0,3/-2)

I don't know if this is right. Now I just don't know where to plot the points. I need help with this. Thank you in advance.
Vet. Asymp. at $x=4$ the bottom is 0 but the tops isnt so it is a vert asymp.

Horiz. asymp. $\lim_{x \to {\pm\infty}}\frac{2x+6}{x-4}=2$...so there is a horiz. asymp at $y=2$

x-int...only when numerator is zero so $2x+6=0\Rightarrow{x=-3}$

y-int... $f(0)=\frac{-3}{2}$