Question 979279: The following rational function describes blood concentration of a certain drug taken via IV overtime, find the horizontal or oblique asymptote if any, the vertical asymptote if any, then tell what possible meanings would this problem relate to the blood concentration of a drug taken via IV overtime with a patient .. F (x) = - 6x-6\ 5x+4 for x >1
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! There is a typo, or at least a failure to understand and/or apply the time-honored conventions on order of operations that are the basis of algebra.
F (x) = - 6x-6/5x+4 = graphs like this 
That function is negative for x >1, so that does not make sense.
If you just forgot that you needed parentheses, and meant
F (x) = - (6x-6)/(5x+4) =  or F (x) = (-6x-6)/(5x+4) =  ,
those functions are also negative for x >1, so they does not make sense either.
If you meant F (x) = (6x-6)/(5x+4) =  , that could make some sense for some drug, at least for the first few hours, or if it is being continuously infused.
 ,
so  , so  is the horizontal asymptote of  ,
and that is the only asymptote that matters for  .
Looking at  as a function without restrictions to its domain,
we may want to graph the function over more of its domain,
and there is, of course, a vertical asymptote for
 <--> <--> :
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