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

$y=\frac{2}{3}$

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

so function is:

$\frac{2(x-3)(x-5)(x-6)}{3(x-6)(x-1)(x-4)}$