Question

Write a rational function $f$ with a slant asymptote $y=x+4$, a vertical asymptote at $x=5$ and one of the zeros at $x=2$.

Answer 1

vertical asymptote, the denominator must contain $(x-5)$

and for zeros the numerator must contain $(x-2)$

So far $f\left(x\right)=\frac{x-2}{x-5}$

For slant asymptote, quotient of numerator divided by denominator must be $(x+4)$

Therefore:

$f\left(x\right)=\frac{(x+4)(x-2)}{x-5}$

So $f\left(x\right)=\frac{x^2+2x-8}{x-5}$