Question

Write a rational function that has a vertical asymptote at = 6, a horizontal asymptote
= −2 and a zero at = −1​

Answer 1

Answer:

since the , rational function f has the vertical asymptote at x=4, then the denominator of f contains the term (x−4).

Thus function f(x) is of the form f=

x−4

g(x)

Since the horizontal asymptote exists y=5, the numerator g(x) of f(x) has to be of the same degree as the denominator with a leading coefficient equal to 5.

Also g(x) must contain the term (x+7) since f has zero at x=−7.

Hence, f(x)=

(x−4)

5(x+7)