Write a possible rational function h with a hole at x = 5, a vertical asymptote at x = -1, a horizontal asymptote at y = 2 and x-intercept at x = 2.

Explanation

The graph of f has a slant asymptote y=x+4 and a vertical asymptote at x=5 , hence f(x) may be written as `f(x)=(x+4)+(a)/((x-5))`,
where a is a constant to be determined using the fact that `f(2)=0` since f has a zero at x=2.
`f(2)=(2+4)+(a)/(2-5)=0:. a=18`
Hence f(x) is given by `f(x)=(x+4)+(18)/(x-5)=(x^(2)-x-2)/(x-5)`
Check the characteristics of the graph of f shown below.