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

Since h has a hole at x = 5 , both the numerator and the denominator have a zero at x = 5. Also the vertical asymptote at at x = -1 means the denominator has a zero at x = -1. An x-intercept at x = 2 means the numerator has a zero at x = 2 . Finally, the horizontal asymptote y = 2 means that the numerator and the denominator have equal degree and the ratio of their leading coefficients is equal to 2. Hence
`h(x)=(2(x-5)(x-2))/((x-5)(x+1))`
The graph of h is shown below, check the characteristics.