Question

write a function with the given characteristics, A rational function with vertical asymptote x=5 and horizontal asymptote y=1/2

Answer 1

A rational function has vertical asymptotes where the denominator is equal to zero.
When the degrees of the numerator and the denominator are the same, then the horizontal asymptote is found by dividing the leading terms, so the asymptote is given by:

y = (numerator's leading coefficient) / (denominator's leading coefficient)

Answer 2

Try
\[

y= \frac {x}{2(x-5)}

\]
or
\[
y= \frac {x+7}{2(x-5)}\\

y= \frac {x-11}{2(x-5)}\\






\]