Question

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

Answer 1

In the forms

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

Answer 2

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

Answer 3

@Nnesha

Answer 4

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

Answer 5

Ok, i'll give the example..

\[y=\frac{ 3 }{ x-2 }+5\]

Answer 6

If im not mistaken, in that form...

x=h
y=k

?

Answer 7

for range and domain?

Answer 8

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

Answer 9

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

Answer 10

Just play with it, move the sliders around.

Answer 11

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

Answer 12

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

Answer 13

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?

Answer 14

That should clear it up for that form

Answer 15

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

Answer 16

How would I write that?

domain=
\[(-\infty,2)(2,\infty)\]

Answer 17

Sorry, was afk

Answer 18

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

Answer 19

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

Answer 20

Looks good. What about for something in the form

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

Answer 21

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

Answer 22

Not in my notes..

Answer 23

hmm

Answer 24

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

right?

Answer 25

For the domain, the denominator cant be zero, so

\[cx+d \neq0~~~~or~~~~x \neq \frac{ -d }{ c }\]

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

7x + 6 cant be 0

Answer 31

-6/7 times 7=-6

Answer 32

-6+6=0

Answer 33

right, x can't be -6/7,

take limit from right and left, one is +infinity one is -infinity

Answer 34

Hmm ok.

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

Answer 35

yeah

Answer 36

Looks clear now, thanks again dude

Answer 37

let x go to infinity,

first divide everything by x

Answer 38

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

Answer 39

horizontal axmptopeas, i cant spell it

Answer 40

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

Answer 41

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

Answer 42

D: { x vertical line x not equal a}

Answer 43

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

Answer 44

i see

Answer 45

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

Answer 46

Definitely gonna use that algebra sheet, thanks