Question

Write an equation for a rational function with:

Vertical asymptotes at x = 3 and x = -4

x intercepts at x = -1 and x = 5

Horizontal asymptote at y = 6

Answer 1

Making a fraction is the easiest way to do this.

The x-intercepts give solutions to a problem that equals zero.

`0 = (x-5)(x+1)`
The vertical asymptotes are values x cannot be, in a fraction the denominator can not be zero.

`y = ((x-5)(x+1))/((x+4)(x-3))`
Horizontal asymptotes are the values y approaches. This can be accomplished by making the leading term have a coefficient of 6

`y = (6(x-5)(x+1))/((x+4)(x-3))`