Does anybody know a lot about graphing rational equations (Senior math)?

Question

phi · Answer

You should post a specific question

anonymous · Answer

How about do you know how to work out the problem: $$f(x)=\frac{ 3x-1}{ x+2 }$$

jack1 · Answer

sorry... what did u need to work out about this eqn...?
do u just need to graph it?

anonymous · Answer

I have worked the problem all the way to where you chart it, but when it comes to actually graphing it and the Horizontal Asymptote I get confused.

jack1 · Answer

ok... so it's really just a line (x value or y value) that your graph will never touch

so look at ur equation

if you divide by 0, you get infinity... right?

so what happens in ur eqn if you put  x = -2?

anonymous · Answer

I really don't know. I am failing my math course, I don't understand much of math IV.

jack1 · Answer

k, no this one's pretty simple, just watch a sec, you'll get it

$\Large f(x)=\frac{ 3x-1}{ x+2 }$

$\Large f(\color{red}{-2})=\frac{ 3\color{red}{(-2)}-1}{ \color{red}{(-2)}+2 }$


$\Huge f(-2)=\frac{ -6-1}{ -2+2 } = \frac{ -7}{\color{blue}{ 0} }$

... cant divide by zero... as y = infinity, so verticle asymtote is at x = -2

follow ok so far?

anonymous · Answer

Yes i follow.

jack1 · Answer

coolski,
now :

$\Large f(x)=\frac{ 3x-1}{ x+2 }$

what happens if y = 3...?

jack1 · Answer

ie f(x) = 3

anonymous · Answer

Can I get back to you on this, my class is leaving.

jack1 · Answer

k nite

jack1 · Answer

sorry its 1am, bailin' soon, so i'm gonna explain, an you just check back when you can?

anonymous · Answer

Lol ok. Its 11:03 am here.

jack1 · Answer

$\Large f(x)=\frac{ 3x-1}{ x+2 }$

can be written as

$\Large y=\frac{ 3x-1}{ x+2 }$

or

$\Large ( x+2 )y={ 3x-1}$

so if y = 3...

$\Large ( x+2 )y={ 3x-1}$

$\Large ( x+2 )\color{red}y={ 3x-1}$

$\Large ( x+2 )\color{red}3={ 3x-1}$

$\Large  3x+6 ={ 3x-1}$

now solve for x...

$\Large  3x+6 ={ 3x-1}$ 

now bring all the like terms to the same side, so first the x's over to the right hand side, by subtracting 3x from both sides...

$\Large  3x+6 \color{red}{-3x}= 3x-1 \color{red}{-3x}$

$\Large  6 =-1$

6 doesn't equal -1, so making y = 3 screwed up the whole equation.... so y = 3 is the horizontal asymptote.... you with me?

jack1 · Answer

example graph attached... see how it curves towards but never touches x = -2
also y = +3
... anyways, good luck and g'nite

anonymous · Answer

@Jack1 thanks for the help. It helped me understand it a little more.

jack1 · Answer

welcomes ;)