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

Ok, one step at the time.

First the a) assignment.
Definition of horizontal asymptote: A horizontal asymptote is a y-value which a function approaches but does not actually reach.

To find it we have to remove everything except biggest exponents in numerator and denominator in given function:

\[f(x) = \frac{ x+1 }{ x } \]

Biggest exponent of x is x^1 found in both numerator and denominator, so we have:

\[f(x) = \frac{ x }{ x }\]

Both numerator and denominator have same exponent of x, so they cancel each other out, and we are left with 1/1, which is 1.

Horizontal asymptote is 1.

Answer 2

Thank you so much...... your the best!!!!

Answer 3

I might need more help.. I hope you don't mind......

Answer 4

sure, one step at the time;) feel free to ask if you don't understand any part of this solution.
here is a good reference for horizontal asymptotes if you need more info:
http://www.freemathhelp.com/finding-horizontal-asymptotes.html

Answer 5

now the b) part
Definition of vertical asymptote: Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function.

As you can see from the definition, we have to find values when will the denominator of our given function be zero in order to find vertical asymptotes.

\[f(x) = \frac{ x+1 }{ x }\]

Denominator is x, and it will be zero when x=0.
Hence, vertical asymptote is 0.