Question

Write a rational function that has zeros at -1 and 3 and vertical asymptote at x=0

Answer 1

We know that any function will have x=0 as verfical asymptote in there is a term of x in denominator, upon substitution of x=0, the denominator becomes 0 and the function will not have a finite value at x=0

e.g: 1/x, x=0 is vertical asymptote of this function as there is no finite value defined over x=0.

a function having zeros at x = -1 and x =3 implies,

the function is factorized as (x+1)(x-3)

implies, x²-2x-3

Combining both, we get the rational function that has zeros at -1 and 3 and vertical asymptote at x=0

is the answer. which has zeros at =1 and 3 with vertical asymptote at x = 0