Question

The following rational function describes concentration in blood of a certain medicine taken once depending on time, find:
A) the horizontal or oblique asymptote
B) the vertical asymptote, if any
C) describe their meanings
f(x)=x/x^2-100

Answer 1

Since x has degree less than x^2-100, the horizontal asymptote is y=0

since x^2-100 = 0 at x = ±10, and x≠0, those are the vertical asymptotes

I find the function unrealistic. It implies negative concentrations, going off the charts as time increases. I suspect a function like x/(x^2+100) would be more like it. It starts with zero concentration, builds up as the pill is digested, and then tapers off at the medicine is metabolized.