Question

Find the equations of both the vertical and horizontal asymptotes of the function: f(x)=(3x-1)/(x+4)

Answer 1

would the vertical be x=-4 and the horizontal would be x=1

Answer 2

the horizontal would be at y=3, and the vertical at x=-4

Answer 3

ok, i see how you got the -4 but why is the horizontal 3

Answer 4

there powers of x are the same, that means that the horizontal asympotote is the ratio of the coefficietnts of the x. In other words 3/1

Answer 5

ok

Answer 6

\[f(x)=\frac{3x-1}{x+4}*\frac{\frac{1}{x}}{\frac{1}{x}}=\frac{\frac{3x}{x}-\frac{1}{x}}{\frac{x}{x}+\frac{4}{x}}=\frac{3-\frac{1}{x}}{1+\frac{4}{x}}\]
what happens as x get really really big?

Answer 7

i'll say that 1/x and 4/x go to zero, is that right?

Answer 8

yes!

Answer 9

yes!!!

Answer 10

and 3 and 1 are constants so they stay the same no matter what changes in x happens

Answer 11

boy, i had to fire up the old noggin for that one

Answer 12

so if the powers of x arent the same for exp: g(x)=(x+7)/x^2 -4), then it would 1/2 horizontal:1 and vertical:2

Answer 13

or

\[\frac{3x-1}{x+4}=\frac{3x+12-12-1}{x+4}=\frac{3(x+4)-13}{x+4}=\frac{3(x+4)}{x+4}-\frac{13}{x+4}=3-\frac{13}{x+4}\]

letting \[x\to\infty\] we get 3

Answer 14

in other words:
\[\lim_{x \rightarrow \infty}f(x)=\frac{3-0}{1+0}=3/1=3\]

Answer 15

thats another one we could do long division! :)

Answer 16

it is the long way though...your way is faster

Answer 17

i was wrong right?

Answer 18

lagrange was right

Answer 19

in that second case, we see that the denominator has a higher power than the numerator, so the horizontal asymptote is at y=0

Answer 20

oh i was fixing to say what
i didn't realize we started talking about another function

Answer 21

sorry, i meant was i right about the 2nd one

Answer 22

no the horizontal asy is wrong
and you are missing a veritcal asy

Answer 23

what lagrange said about the horizontal asy is correct

Answer 24

when is x^2-4, 0?

Answer 25

do this: x^2-4=0

Answer 26

so you said x was 2
is there another x that makes x^2-4=0?

Answer 27

i will take a wild guess: -2?

Answer 28

judges?

Answer 29

yes ;)

Answer 30

you win a brand new tv

Answer 31

sweet...is it 3D

Answer 32

sure

Answer 33

nice

Answer 34

so you have 2 vertical asy
one is x=2
another is x=-2

Answer 35

ok i'm gonna play some video games now

Answer 36

you guys have fun
i might look in every once in awhile

Answer 37

later...have fun!

Answer 38

catch you later

Answer 39

ok, later, thanks for the help.

Answer 40

lol

Answer 41

lol

Answer 42

hi anyone knows chemistry???

Answer 43

u knw it???

Answer 44

k i will post it....plz explain too