SOLUTION: Write an equation for a rational function with: Vertical asymptotes at x = -6 and x = 5 x intercepts at x = -4 and x = -3 Horizontal asymptote at y = 7

This rational function wants to have binomial factors (x+6) and (x-5)
in the denominator to provide the necessary asymptotes

and binomial factors (x+4) and (x+3) in the numerator to provide the necessary x-intercepts.


So, we write

    f(x) = 


with coefficient "a".


Horizontal asymptote y= 7 means that  { limit f(x) }  is 7 when x tends to +oo  or -oo,
which means that a= 7.


Finally, the function is  f(x) = .    ANSWER