The question asks for the left-hand limit as $x$ approaches 7 from the left, or:

$\lim_{x \to 7^-} f(x)$

Looking at the graph provided, we can observe the behavior of the function $f(x)$ as $x$ approaches 7 from the left-hand side:

• As $x$ approaches 7 from the left, the function $f(x)$ is moving upward and seems to approach the value $1$ just before $x = 7$.
• The value of $f(7)$ itself is not relevant since we only care about the value as $x$ approaches 7 from the left (denoted by $7^-$).

Thus, the left-hand limit is:

$\lim_{x \to 7^-} f(x) = 1$

The correct answer is $\boxed{1}$.

Would you like more details on this, or do you have any further questions?

Here are five questions that can further expand on the concept:

1. What is the right-hand limit of $f(x)$ as $x \to 7^+$?
2. How do you interpret the overall limit $\lim_{x \to 7} f(x)$?
3. What happens if the left-hand and right-hand limits are not equal?
4. How does a discontinuity affect the limit of a function?
5. Can a function have a limit at a point even if it's not defined at that point?

Tip: When calculating limits from the graph, focus on the behavior of the function near the point of interest, not the actual value at that point!