Do the functions, which do not approach infinity, also have limiting values?

Question

The above graph shows that its $y$ value is always $\pm4$ when $x$ approaches $\pm\infty$.

So, what would be the value of, say, $\lim\limits_{x \to 4} f(x)$?

Is it $4$? Explain why.

Do the functions, which do not approach infinity, have limiting values?

Answer 1

Recall that for a continuos function

$$\lim_{x\to x_0} f(x)=f(x_0)$$

and the given function is continuous at $x=4$.

We can't say nothing for the limit at infinity since we have not sufficient information.