Which of the following statements guarantees that $x=4$ is a vertical asymptote of the function $f(x)$?

I.$\mathop {\lim }\limits_{x \to \infty } f(x) = 4$II.$\mathop {\lim }\limits_{x \to {4^ + }} f(x) = -\infty$III.$\mathop {\lim }\limits_{x \to 4} f(x)$ does not exist

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