Question

The following rational function describes blood concentration of a certain drug taken via IV over 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+1/x

Answer 1

We have the function:
\[f(x)=\frac{ x+1 }{ x }\] Since the degree of the the numerator and denominator are equal (they're both 1) we will have a horizontal asymptote at y=0.
To find vertical asymptotes, set the denominator equal to 0 (since we can't divide by 0) and get x=0.
The horizontal asymptote means that the concentration never reaches 0. The vertical one means at the start with time=0, there is an undefined concentration.