From the graph provided, we need to find the limit of the function $f(x)$ as $x$ approaches $a = -1$. Let's analyze the behavior of the function near $x = -1$:

1. The graph shows a point at $x = -1$ where the function reaches a height of $y = 3$. Additionally, the curve is continuous on both sides of $x = -1$ and appears to approach this same height as $x$ gets closer to $-1$ from both the left and the right.

2. Therefore, the left-hand limit ($\lim_{x \to -1^-} f(x)$) and the right-hand limit ($\lim_{x \to -1^+} f(x)$) both approach the value 3.

Since both one-sided limits are equal, the overall limit exists and is equal to the height of the function at that point.

Answer:

$\lim_{x \to -1} f(x) = 3$

Would you like further details or have any questions?

Related Questions:

1. What is the limit of the function as $x$ approaches $3$ in this graph?
2. How do you determine a limit when there is a discontinuity at a point?
3. What is the difference between one-sided limits and two-sided limits?
4. If the function had a jump discontinuity at $x = -1$, would the limit still exist?
5. How would the limit change if the point at $x = -1$ was an open circle at a different $y$-value?

Tip:

When evaluating limits graphically, always check both the left-hand and right-hand behavior of the function around the point in question.