Question

sketch the graph of

Answer 1

\(y=\frac{x^{2}}{1+x}\)

Answer 2

@kittybasil

Answer 3

How to find Horizontal and Slant Asymptotes How to find Vertical Asymptotes

Answer 4

i found one of the asymptotes which is x=-1
but i'm not sure how to find the other asymptote...

Answer 5

can u show me how to find the slant asymptote?

Answer 6

@kittybasil

Answer 7

x=-1 is your Vertical asymptote, but it seems you figured that out
y=x-1 is the Horizontal, or slant asymptote.
Do you want me to screenshot the graph?

Answer 8

i try insert x=-1 into the eqn,n i got y=undefined
since y is undefined,hence x=-1 is an asymptote

Answer 9

but can u show me how u get y=x-1? @Marziman

Answer 10

It's actually painfully simple, you just apply long division and after dividing, you get a quotient of x-1 with the remainder 1. Therefore your answer is y=x-1

Answer 11

i tried doing that but i got y=x
xD

Answer 12

I will send the working here...
maybe u can detect my error

Answer 13

There's actually a specific rule that pertains to this, let me grab it for you online give me uno momento

Answer 14

okay

Answer 15

If the denominators degree is greater than the numerator's degree then the horizontal asymptote is the x-axis: y=0. Now if the numerator's degree is 1+the denominators degree then the asymptote is a slant asymptote of the form y=mx+b

Answer 16

dude its marz hes right 95% of the time just take it

Answer 17

:)

Answer 18

i know that...
the answer is right but i need to show the working... xD

Answer 19

lmao

Answer 20

Also if the numerators degree is greater than 1+the denominators degree then there isn't a horizontal asymptote
and if the degrees are equal then the asymptote is y= numerators leading coefficient/denominators leading coefficient

Answer 21

Just making sure xD

Answer 22

This is my working...hope u can check where i went wrong...

Answer 23

nice drawing skills lmao

Answer 24

Thanks xD

Answer 25

Took me a minute to figure out what those backwards C's were lol. I can't really tell where you're actually going wrong though...

Answer 26

u mean this?

Answer 27

No, the X's lol

Answer 28

oh okay... xD

Answer 29

OH I SEE the first mistake!

Answer 30

okay,can u pls show me :)

Answer 31

Your quotient is correct, BUT you didn't multiply x^2+x by x+1. After that subtract x^2+x from x^2 to get -X as your remainder.

Answer 32

i'm confused...
can u show me by drawing it

Answer 33

So now you divide -x by x+1

Answer 34

is it like this?

Answer 35

Yes

Answer 36

why is it -x but not x^2

Answer 37

Because x^2 became -x since it's our remainder. Remember, we subtracted x^2 + x from x^2 making -x

Answer 38

oh i c...

Answer 39

makes sense now

Answer 40

So now your quotient is -1 after dividing -x/x = -1
Now multiply x+1 by -1 to get -1-x now all you do is subtract -x-1 from -x and you get a remainder of....1 :D

Answer 41

So your horizontal is y=x-1

Answer 42

oh i get now...
i hvn't completed the working... xD
Thank you! @Marziman

Answer 43

Nah you're all good XD

Answer 44

Not really @Marziman
Thanks for helping me out...
n also thanks to @kittybasil
the links are really helpful...
Thanks guys!! :)

Answer 45

and me for coaching

Answer 46

lol...
yaya,sure... :P