write an equation for the given

Question

Write an equation for a rational function with:

Vertical asymptotes at x = -3 and x = -6

x intercepts at x = 4 and x = 1

Horizontal asymptote at y = 4

Answer 1

Hello

x intercepts at x = 4 and x = 1

So Numerator will be (x-4)(x-1)

Vertical asymptotes at x = -3 and x = -6

so denominator will be (x+3)(x+6)

so y=(x-4)(x-2) /(x+3)(x+6)

here if we expand numerator and denominator degree of both are equal which is 2

In that case horizontal asymptote is ratio of numerator and denominator coefficient

Here Horizontal asymptote at y = 4 =4/1

so

we will write rational function as

y=F(x) = 4(x-4)(x-2) / (x+3)(x+6)