Problema Solution
The following rational function describes concentration in blood of a certain medicine taken once depending on time, find
a) the horizontal or oblique asymptote(s), if any,
b) the vertical asymptote(s), if any,
c) describe their possible meanings
f(x)=x/x^2-100
Answer provided by our tutors
a) Horizontal Asymptote
It is a Horizontal Asymptote when: as x goes to infinity (or to -infinity) then the curve approaches some fixed constant value "b"
f(x)=x/x^2-100
f(x)=1/x - 100
if x goes to infinity y approaches to -100 and y = - 100 is the horizontal aymptote
b) Vertical Asymptotes
It is a Vertical Asymptote when: as x approaches some constant value "c" (from the left or right) then the curve goes towards infinity (or -infinity)
if x goes to 0 then y approaches to infinity that is the vertical asymptote is x = 0
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