The image presents a graph of a function, where you're being asked to evaluate it graphically, and specifically to find $f(1)$.

Analyzing the Graph

• There are two points marked on the graph. One is filled in at $(-2, -1)$, indicating that $f(-2) = -1$.
• The other point is open at $(3, -6)$, meaning that the function does not take the value $f(3) = -6$; it's undefined at $x = 3$.
• The graph behavior suggests that $f(x)$ decreases steeply as $x$ moves from negative to positive values.

Evaluating $f(1)$

From the graph, it appears that $f(1)$ corresponds to $-6$ because the curve passes through the point $(1, -6)$. Therefore: $f(1) = -6$

Would you like more details on interpreting graphical functions or specific insights into other points on the graph?

Here are five related questions to expand on the concept:

1. What is the value of $f(-2)$ based on the graph?
2. What happens to $f(x)$ as $x$ approaches 3?
3. Is $f(3)$ defined or undefined, and why?
4. How does the graph behave for $x < -2$?
5. Can you determine if this function is continuous at $x = 1$?

Tip: When reading a graph, closed dots represent defined values of the function, while open dots indicate points where the function is undefined.