I have mid terms tomorrow, and i completely blanked on how to do this:
I have to find the domain, range, vertical/horizontal asymptote and discontinuities, if any, what kind; removable to or continuous.
I know the vertical asymptote is -2 but how do i find the horizontal ones. i graphed it and the graph did have multiple horizontal asymptotes.
I know what you mean , but I think it encourages the superficial rote learning of a fact, rather than an understanding of the theory behind that fact .... If a student asked does , say, have a horizontal asymptote, I would very much hope that the answer they got used the concept of a limit at some stage .....
first note that the 10 in the denominator is immaterial as x goes to infinity or negative infinity.
also note, that an alternative definition for |x| is
thus we have:
so there are two horizontal asymptotes here
for the vertical asymptotes, find where the function is undefined, that is, where the denominator is zero. such x's are vertical asymptotoes. these are also the x's that are NOT in the domain (among other x's perhaps, here for instance, we have to find out what x's causes the square root to mess up)
are you good on everything else, MathProfessor?