Question

Why do i need a slant asymptote and how can i use it for graphing ?

Answer 1

i cant type complete sentences right now except for this one lol

Answer 2

Yup helps to visualize the graph if u can find 'em...

Answer 3

But for this "\frac{x^3-8}{x^2+5x+6}" The Slant asymptote intersects the surve

Answer 4

\[\frac{x^3-8}{x^2+5x+6}\]

Answer 5

http://www.wolframalpha.com/input/?i= {x^3-8}%2F{x^2%2B5x%2B6}%2C+x%3D+-10++to+0

Answer 6

But here the slant asymptote is also there and it interescts it

Answer 7

The slant asymptote is y = x-5

Answer 8

Slant (or oblique) asymptotes denotes symmetry: one half mirrors the other half. A dead giveaway is usually degree numerator greater than denominator. To identify slant asymptotes use long division. Divide numerator by denominator: the result would be a line, your slant asymptote.

Answer 9

Yes i did and i found it to be interescting the slant asymptote and neither it is symmetric about the SA

Answer 10

I don't understand..

http://www.wolframalpha.com/input/?i= {x^3-8}%2F{x^2%2B5x%2B6}+x%3D-5+to+5+y+%3D+-20+to+20

Answer 11

By Solvin I got the slant asymptote as y=x-5.But the curve interescts the that line.But according to asymptotes they should not intersect with the curve.I'm Not talking about Vertical / Horizontal Asymptotes

Answer 12

sometime the curve does go through the asymptote

Answer 13

it never goes through vertical asymptote

Answer 14

You don't have the common graph that we are describing that is usually associated with a slant asymptote. What you have is a curve which becomes a straight line.

Answer 15

But look at this the Curve should not pass through the slant asymptote as well http://en.wikipedia.org/wiki/Asymptote#Oblique_asymptotes

Answer 16

That curve from wiki doesn't 'pass through', it gets infinitely close but never touches.

Answer 17

A curve can pass through a slant asymptote or a horizontal asymptote, but it cannot pass through a vertical one. The reason it cannot pass through a vertical asymptote is because the function is undefined at that point (or there is a jump discontinuity). A slant asymptote usually lets you know what the graph looks like as it goes off to infinity or negative infinity.

Answer 18

@chaguanas Yers i Know that i was proving my point against "myininaya"

Answer 19

that it gets closer but it can also cross

Answer 20

as x goes to infinity the curve gets closer to whatever line we have depending on if we have a slant asymptote
i never said it couldn't cross

Answer 21

Ok.Anyway I still didn't get my answer guys. In all the cases The Slant Asymptote is not touched but only this case its happening where am i going wrong ?

Answer 22

whats the question? im confused

Answer 23

I know it might touch at Infinitey but on finding the slant asymptote and computing the graph for the above it seems to be touching well before infintely.I can see the point on the graph http://graph.tk/

Answer 24

You're not necessarily wrong if it touches the slant asymptote. The function is allowed to touch a slant asymptote or a horizontal one.

Answer 25

right!

Answer 26

the graph can even cross more than once just as long as the graph is getting even closer the the asymptote as x goes to infinity

Answer 27

Then can i trust that the sketch i draw according to my asymptotes is right ? Because usually i would just make sure it doesn't touch it..And that's what every website says

Answer 28

http://answers.yahoo.com/question/index?qid=20091021200054AAwcM2v

Answer 29

If you are drawing a graph it is just a representation, for what they call end behavior you just make an arrow. If you are worried about where it specifically touches there are ways you can find that out. But the slant asymptote is a tool for some general functions.

Answer 30

http://www.purplemath.com/modules/asymtote2.htm

Answer 31

Ok Thanks for that.But for every function i would get a solution for f(x) = SA And moreover should i have to check everytime if it crosses theSA and if so i don't see any point in SA.Whats the main puporse.There is also no symmetry about it !

Answer 32

http://www.sinclair.edu/centers/mathlab/pub/findyourcourse/worksheets/116,117/AsymptotesOfGraphsOfRationalFunctions.pdf

Answer 33

it helps for us to know the end-behavior of the graph to graph it

Answer 34

or maybe i shouldn't say end-behavior...

Answer 35

or maybe i should

Answer 36

Saikrishnadeep, you chose one that has no symmetry. It is like studying Spanish or a foreign language, the verbs all conjugate the same, except, there are some irregular ones.

Answer 37

lol

Answer 38

@chaguanas Then i don't see anypoint on learning it ! Thanks for your help anyway ! Really aprreciate this debate :D

Answer 39

That article really helped me a lot :DF

Answer 40

what article

Answer 41

I still don't understand this, the line y = x-5 is slant asymptote to the curve in the third quadrant and as far as I can see, it doesn't cross the curve.