Answer
$\lim_{x \to 0 }f(x)$ does not exist.
Work Step by Step
To find $\lim_{x\to 0 }f(x)$, examine the graph of $f$ near $x=0$. As $x$ gets closer to $0$ from the left, the values of $f(x)$ get closer to $4$. As $x$ gets closer to $0$ from the right, the values of $f(x)$ get closer to $5$. We conclude from the graph that $\lim_{x \to 0 }f(x)$ does not exist because the left- and right-hand limits are unequal.
