Question

Find the vertical asymptotes, if any, of the graph of the rational function. Show your work. f(x) = x-4x(x-4)

Answer 1

vertical asymptotes are the values that "x" cannot be. You can find these by:

(1) simplifying the numerator and denominator and then and setting the denominator equal to zero ... in your problem, there is no denominator.

(2) setting the inside of the square root less than 0 ... in your problem, there is no square root.

Since neither of these apply to your problem, there are no vertical asymptotes.

Answer: none

FYI: If you wrote the problem wrong and it is supposed to be f(x) =
`(x-4x)/(x - 4)`, then the factored form is f(x) =
`(x(x - 4))/(x - 4)` and the simplified form is f(x) = x.

The answer would still be "none" because neither (1) or (2) above apply.