Question

Write a function that fits the following criteria: 1. Vertical asymptotes at x = 1 and x = 42. Zeroes at 3 and 53. Hole when x = 64. Horizontal asymptote at y = 2/3

Answer 1

At zero x=3 and x=5 that mean factor in numerator is:

`(x-3)(x-5)`

a hole x=6 that mean factor in boath numerator and denominator is:

`(x-6)`

a vertical asymptotes is:x=1 and x=4 that mean factor in denominator is:

`(x-1)(x-4)`

the horizontal asymptote is

`y=(2)/(3)`

mean hogher degrees in boath denominator and numeratore is are equal and their coefficient is 2:3

so function is:

`(2(x-3)(x-5)(x-6))/(3(x-6)(x-1)(x-4))`