To find the limit $\lim_{x \to 1^-} f(x)$ from the given graph, we need to analyze the behavior of the function $f(x)$ as $x$ approaches $1$ from the left side (i.e., from values less than 1).

Looking at the graph:

• As $x$ approaches 1 from the left ($x \to 1^-$), the value of $f(x)$ is moving towards a specific point on the graph.
• We need to locate the point just before $x = 1$ and see the corresponding $y$-value on the graph.

On the graph:

• When $x$ is slightly less than 1 (coming from the left), the graph shows that $f(x)$ is approaching the $y$-value of 2.

Therefore, the limit is: $\lim_{x \to 1^-} f(x) = 2$

Would you like further details or have any questions? Here are five related questions that expand on this topic:

1. How do you determine $\lim_{x \to 1^+} f(x)$ from the graph?
2. What is the importance of one-sided limits in calculus?
3. How can we determine if a function is continuous at a point using limits?
4. What is the difference between $\lim_{x \to 1^-} f(x)$ and $\lim_{x \to 1^+} f(x)$?
5. How do you find the overall limit $\lim_{x \to 1} f(x)$ if both one-sided limits are equal?

Tip: When analyzing limits from a graph, always carefully observe the function's behavior as it approaches the specified point from the left and the right separately.