Question

Write an equation for a function that has zeros at (4, 0) and (-1,0), has a vertical asymtote at x=3, and a hole at x=5
Anyone who helps me with this is awesome

Answer 1

for there to be zeros at (4,0) and (-1,0) the function will need to have(x-4)(x + 1) in the numerator
an (x - 3) in the denominator will give a vertical asymptote at x = 3

for a hole at x = 5 we must have (x-5) in numerator and denominator


so our function is

f(x) = (x+1)(x-4)(x-5)
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(x-3)(x-5)