To determine the value of $h(2)$ from the graph, we need to find the point on the piecewise function where $x = 2$.

1. The first line segment starts from approximately $(-4, 2)$ and moves downwards.
2. The second line segment appears to connect points near $(3, 3)$ and $(5, 5)$, but this doesn't concern $x = 2$.

Let's focus on the point for $x = 2$:

• The first line segment intersects the x-axis near $x = 2$ and has a corresponding $y$-value of $-1$.

Thus, $h(2) = -1$.

Answer:

The value of $h(2)$ is $-1$.

Would you like more details or clarifications?

Here are five related questions to explore:

1. How do you determine the equation of the line segments in a piecewise function from a graph?
2. What is the domain of this piecewise function based on the graph?
3. What is the range of the first segment of the function?
4. How do you find where the function is increasing or decreasing from the graph?
5. How does a piecewise function differ from a regular linear function?

Tip: When interpreting piecewise functions, always pay attention to whether the points are filled or open, indicating whether they include or exclude certain values of $x$.