The graph appears to show a step function defined piecewise, where different intervals of $x$ correspond to constant values of $y$. The blue dots indicate inclusive and exclusive endpoints, suggesting which intervals are included or excluded.

Let me analyze the details and write the piecewise function:

1. From the graph:

   • The step starts at $x = 0$ (closed dot), $y = 0$.
   • At $x = 3$ (open dot), $y$ moves to $1$.
   • Then, $y = 1$ remains constant until $x = 5$ (closed dot).

2. Piecewise Function:

   \begin{cases} 0 & \text{if } 0 \leq x < 3, \\ 1 & \text{if } 3 \leq x \leq 5. \end{cases}$$

Would you like a detailed explanation of how this function is derived, or do you have specific questions? Here are some related questions:

5 Related Questions:

1. How do you determine the equations for piecewise functions from a graph?
2. What do open and closed dots on a graph signify mathematically?
3. How would the function change if the open and closed dots were swapped?
4. How can this piecewise function be expressed using the Heaviside step function?
5. What is the significance of step functions in real-world applications?

Tip:

When analyzing piecewise functions, always check the continuity and inclusion/exclusion of endpoints by noting open (excluded) and closed (included) dots.