rational function help

Question

Hello, does anyone know a rational function that has a:

vertical asymptote at x = 3 and x = 4

x-intercept at x = 1 and x = -4

y-intercept = 4

I am very confused and would greatly appreciate the help! :)

Answer 1

-12 (X-1)(x+4)

Y= ------------------------

(x-3)(x-4)

Vertical asymptote means the number is not on the domain because of division by zero...

Given that x=3 and x=4 make the denominator zero, x-3 and x-4 are in the denominator

X-intercept means y=f(x)=0 for the given value of x. The given x-intercepts are 1 and -4, so x-1 and x+4 must be in the numerator

Finally this fraction is -1/3 when x=0.

So in order to get it equal to 4, it must multiply by -12

Answer 2

Vertical asymptotes would be when (x-3) and (x-4) are n the denominator as the function is undefinable at these values( can’t divide by 0)

If the zeros or x intercepts are at 1 and -4 then (x-1)and (x+4) x-1 are in the numerator

So equation is y= (a)(x-1)(x+4)/(x-3)(x-4) Now just nee o solve for a

If the y intercept is 4 then the graph contains the point (0,4) which we can use to solve he above equation

4= a(-1)(4)/(-3)(-4)

48=-4a

a=-12

y=-12(x-1)(x+4)/((x-3)(x-4)