To determine $\lim_{x \to 0} f(x)$ from the given graph, we need to analyze the behavior of the function $f(x)$ as $x$ approaches 0 from both the left ($x \to 0^-$) and the right ($x \to 0^+$).

• As $x \to 0^-$ (approaching 0 from the left): The graph shows that as $x$ gets closer to 0 from the negative side, the function $f(x)$ approaches 2.

• As $x \to 0^+$ (approaching 0 from the right): The graph indicates that as $x$ gets closer to 0 from the positive side, the function $f(x)$ also approaches 2.

Since both the left-hand limit and the right-hand limit as $x$ approaches 0 are equal and both equal to 2, we conclude:

$\lim_{x \to 0} f(x) = 2$

Would you like more details or have any other questions?

Here are some related questions:

1. What is the definition of a limit in calculus?
2. How do you find the limit of a function graphically?
3. What is the significance of one-sided limits?
4. How do discontinuities affect the existence of limits?
5. Can a function have a limit at a point where it is not defined?

Tip: When determining limits graphically, always check the behavior of the function from both sides of the point in question to ensure consistency in the limit value.