OpenStudy (dtan5457):

Someone refresh me on finding vertical and horizontal asymptotes of rational functions.

2 years ago
OpenStudy (dtan5457):

In the forms \[y=\frac{ a }{ x-h }+k\]

2 years ago
OpenStudy (dtan5457):

and \[y=\frac{ ax+b }{ cx+d }\]

2 years ago
OpenStudy (dtan5457):

@Nnesha

2 years ago
OpenStudy (dtan5457):

Someone just give me an example of anything each in that form..

2 years ago
OpenStudy (dtan5457):

Ok, i'll give the example.. \[y=\frac{ 3 }{ x-2 }+5\]

2 years ago
OpenStudy (dtan5457):

If im not mistaken, in that form... x=h y=k ?

2 years ago
OpenStudy (dtan5457):

for range and domain?

2 years ago
OpenStudy (kainui):

https://www.desmos.com/calculator/9nmsk6oerv

2 years ago
OpenStudy (dtan5457):

@Kainui In your example, is the domain all real numbers except for 3.8? And range as well?

2 years ago
OpenStudy (kainui):

Just play with it, move the sliders around.

2 years ago
OpenStudy (danjs):

The function will have a vertical asymptote at a value x=a, if \[\lim_{x \rightarrow a^-}(x) = \pm \infty \]\[\lim_{x \rightarrow a^+}f(x) = \pm \infty\]\[\lim_{x \rightarrow a}(x) = \pm \infty\]

2 years ago
OpenStudy (dtan5457):

I know A doesn't really affect the domain and range, I just want to know if for your specific example if I had the domain and range correct

2 years ago
OpenStudy (dtan5457):

Dan, can you just check for my example I gave. Is the domain all real numbers except for 2, and range is all except for 5?

2 years ago
OpenStudy (dtan5457):

That should clear it up for that form

2 years ago
OpenStudy (danjs):

The function will have a horizontal asymptote at Y=# if the function approaches a value # as x goes to + or - infinity.

2 years ago
OpenStudy (dtan5457):

How would I write that? domain= \[(-\infty,2)(2,\infty)\]

2 years ago
OpenStudy (danjs):

Sorry, was afk

2 years ago
OpenStudy (danjs):

Yeah, Domain of f(x) is all x such that x does not equal h

2 years ago
OpenStudy (danjs):

\[[~x ~| ~~x ~\epsilon ~R ,~ and ~x \neq h]\]

2 years ago
OpenStudy (dtan5457):

Looks good. What about for something in the form \[y=\frac{ ax+b }{ cx+d }\]

2 years ago
OpenStudy (dtan5457):

Wasn't there a specific formula to get domain and range for that?

2 years ago
OpenStudy (dtan5457):

Not in my notes..

2 years ago
OpenStudy (danjs):

hmm

2 years ago
OpenStudy (dtan5457):

Oh. y=a/c x=-d/c right?

2 years ago
OpenStudy (danjs):

For the domain, the denominator cant be zero, so \[cx+d \neq0~~~~or~~~~x \neq \frac{ -d }{ c }\]

2 years ago
OpenStudy (danjs):

the domain would be all real numbers x, except x cant be -d/c

2 years ago
OpenStudy (danjs):

The range would be all the Y values you get from the domain

2 years ago
OpenStudy (dtan5457):

\[y=\frac{ 5x+2 }{ 7x+6 }\]

2 years ago
OpenStudy (dtan5457):

So for this domain would be all except for -6/7?

2 years ago
OpenStudy (danjs):

7x + 6 cant be 0

2 years ago
OpenStudy (dtan5457):

-6/7 times 7=-6

2 years ago
OpenStudy (dtan5457):

-6+6=0

2 years ago
OpenStudy (danjs):

right, x can't be -6/7, take limit from right and left, one is +infinity one is -infinity

2 years ago
OpenStudy (dtan5457):

Hmm ok. And for range...just all except for 5/7?

2 years ago
OpenStudy (danjs):

yeah

2 years ago
OpenStudy (dtan5457):

Looks clear now, thanks again dude

2 years ago
OpenStudy (danjs):

let x go to infinity, first divide everything by x

2 years ago
OpenStudy (danjs):

\[\lim_{x \rightarrow \infty}\frac{ 5 + \frac{ 2 }{ x } }{ 7+\frac{ 6 }{ x } } = \frac{ 5 }{ 7 }\]

2 years ago
OpenStudy (danjs):

horizontal axmptopeas, i cant spell it

2 years ago
OpenStudy (danjs):

as x goes to infinity , y goes to 5/7

2 years ago
OpenStudy (dtan5457):

so if on a test, I shouldn't write all real numbers except for #?

2 years ago
OpenStudy (danjs):

D: { x vertical line x not equal a}

2 years ago
OpenStudy (danjs):

all x, such that x does not equal #, the number being the vertical asmyptote

2 years ago
OpenStudy (dtan5457):

i see

2 years ago
OpenStudy (danjs):

2 years ago
OpenStudy (danjs):

2 years ago
OpenStudy (dtan5457):

lol damn I hope that is not necessary. only in alegebra2/trig...never seen this in my life

2 years ago
OpenStudy (danjs):

2 years ago
OpenStudy (dtan5457):

Definitely gonna use that algebra sheet, thanks

2 years ago
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