To estimate $g(3)$ using the graph of the function $g(x)$:

1. Locate the point on the $x$-axis where $x = 3$.
2. Trace vertically from $x = 3$ until you reach the point on the graph that corresponds to this $x$-value.
3. Observe the $y$-coordinate of this point to estimate $g(3)$.

From the graph, at $x = 3$, the $y$-value appears to be around 1. This suggests that: $g(3) \approx 1$

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

Here are some related questions to deepen understanding:

1. How would you find $g(x)$ for values not clearly shown on the graph?
2. What does the slope of each segment indicate about $g(x)$?
3. How can you determine if $g(x)$ is continuous at $x = 3$?
4. What would $g(4)$ be, based on this graph?
5. How can the domain and range of $g(x)$ be determined from this graph?

Tip: Always check the behavior of the graph near the point of interest to ensure accurate estimations, especially if the function is piecewise or has discontinuities.