Question

Write an equation for a rational function with:
Vertical asymptotes at x = 5 and x = 4
x-intercepts at x = 2 and x = 1
Horizontal asymptote at y = 7

Answer 1

Answer:

  $f(x)=\dfrac{7(x-1)(x-2)}{(x-4)(x-5)}$

Step-by-step explanation:

In order for the function to have vertical asymptotes at x=5 and x=4, the denominator factors must include (x-4) and (x-5).

In order for the function to have zeros at x=2 and x=1, the numerator factors must include (x-1) and (x-2).

In order for the horizontal asymptote to be 7, the ratio of highest-degree terms in numerator and denominator must be 7. The function shown above and on the graph meets your requirements.