Write a rational function.?

Question

Write a rational function that has the following properties...

- a zero at x= 4

- a hole at x= 7

- a vertical asymptote at x= -3

- a horizontal asymptote at y= 2/5

Answer 1

-a zero at x = 4:  one of its factors must be (x - 4)

-a hole at x = 7:  the only way I can see to do this without creating a vertical asymptote at 7 is to explicitly restrict the domain to x | x does not equal 7

-a vertical asymptote at x = -3:  one of the factors of the denominator must be (x + 3)

- a horizontal asymptote at y = 2/5:  the degree of the numerator must be the same as the degree of the denominator.  Then, just put 2 in the numerator and 5 in the denominator.

So:

f(x) = 2(x - 4)/[5(x + 3)], x does not equal 7

Just out of curiosity, United States Coast Guard or University of Spoiled Children?