From the image, I can see two mathematical expressions related to a graph that involves a function $f(x)$.

1. $f(2) = -1$
2. $\lim_{x \to 2} f(x) = 2$

Let's analyze each part:

a) $f(2) = -1$

This expression tells us that when $x = 2$, the value of the function $f(x)$ is $-1$. This represents a specific point on the graph, namely $(2, -1)$.

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

This expression represents the limit of the function $f(x)$ as $x$ approaches 2. The limit being 2 means that as $x$ gets closer to 2 (but not necessarily equal to 2), the function approaches the value 2.

Interpretation:

• The limit and the actual function value at $x = 2$ are not the same. This suggests a discontinuity at $x = 2$. Specifically, this could indicate a jump discontinuity, where the function "jumps" from one value to another at $x = 2$.

Would you like further clarification on any of these points?

5 Related Questions:

1. What is the difference between a limit and the actual function value at a point?
2. How can a graph have a limit at a point but not be continuous?
3. What are different types of discontinuities in a function's graph?
4. How do you evaluate limits for more complex functions?
5. How does a jump discontinuity affect the behavior of a graph?

Tip: To identify a discontinuity, always check both the limit as $x$ approaches the point and the actual function value at that point.