
Finding Verticle asymptotes, holes and, and horizontal asymptotes
im having a really difficult time finding out how to find the verticle asymptote and holes and horizontal asymptote. its really frustrating (Headbang)
for exmaple here are some questions:
http://www.webassign.net/latexImages...619c1726cf.gif
http://www.webassign.net/latexImages...cdd4b9eb44.gif
http://www.webassign.net/cgiperl/sy...28x%20%203%29
thank you in advance

Re: Finding Verticle asymptotes, holes and, and horizontal asymptotes
let's start with something simple to see what you know ...
where are the vertical asymptotes?
what is the horizontal asymptote?
where is the point discontinuity (hole) ?

Re: Finding Verticle asymptotes, holes and, and horizontal asymptotes
out of my little understanding of it (my instructor sucks)
i can say that
horizontal asymptote at 1/2
vertical asymptotes at 1,2, and 3
holes at........i dont even know. LOL

Re: Finding Verticle asymptotes, holes and, and horizontal asymptotes
Quote:
Originally Posted by
Recyclop out of my little understanding of it (my instructor sucks)
i can say that
horizontal asymptote at 1/2
vertical asymptotes at 1,2, and 3
holes at........i dont even know. LOL
horizontal asymptote at y = 1/2 ... it's the equation of a line
vertical asymptotes at x = 1 and x = 3 , "hole" at x = 2 ... note the common factor in the numerator and denominator.
OK ... using one of your problems
horizontal asymptote at y = ?
two vertical asymptotes ... where?
one "hole" ... where?

Re: Finding Verticle asymptotes, holes and, and horizontal asymptotes
so horizontal asymptote @ y=6
verticle asymptotes at x=+2 and x=2
the hole would be at.....X^2 would be the only common factor i see. but that would be sqrt0.... so there is no hole?

Re: Finding Verticle asymptotes, holes and, and horizontal asymptotes
horizontal asymptote is y = 0 ... the degree of the numerator < degree of the denominator
vertical asymptotes correct
hole at x = 0

Re: Finding Verticle asymptotes, holes and, and horizontal asymptotes
so after class today i got a good understanding of asymptotes and what not.
only thing that still doesnt make sense is holes. i understand that a hole occurs when you have common factors but what do i do to find the point and what does a hole mean?

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Re: Finding Verticle asymptotes, holes and, and horizontal asymptotes
A "hole" is really a point discontinuity ... the discontinuity occurs at the xvalue that makes the common factor in the numerator and denominator equal to zero.
for example, the function has a "hole" at . the graph of the function will look like the line except for the "hole" at ...
note the graph made on my TI calculator ... see the "hole" ?

Re: Finding Verticle asymptotes, holes and, and horizontal asymptotes
ya i see, so how do we determine the y value? is it just whatever number happens to be there if we plug in 1 for the complete function?

Re: Finding Verticle asymptotes, holes and, and horizontal asymptotes
sub in x = 1 after dividing out the common factor ... in this case, y = x+1 = 1 + 1 = 2 ... the "hole" is at (1,2).

Re: Finding Verticle asymptotes, holes and, and horizontal asymptotes
so if there are holes, are the common factors canceled first? then there would be no Vertical asymptotes?

Re: Finding Verticle asymptotes, holes and, and horizontal asymptotes
the function has both a hole at one xvalue and a vertical asymptote at another xvalue ... where?

Re: Finding Verticle asymptotes, holes and, and horizontal asymptotes
hole at 1/2. but would 3 and 1 still be verticle asymptotes and would 1 still be a root?

Re: Finding Verticle asymptotes, holes and, and horizontal asymptotes
sorry, but no ...
there is a hole at x = 1 (the value of x that makes the factor common to the numerator and denominator 0), the yvalue of the hole is 3/4
there is one vertical asymptote at x = 3

Re: Finding Verticle asymptotes, holes and, and horizontal asymptotes
ok i see now, thank you very much!