Short Answer 
A step graph is composed of horizontal segments each 1 unit long, featuring closed circles on the left (included) and open circles on the right (not included). By starting at point (–3, –5) and systematically moving up and right, the graph is constructed leading to (5, 2) while the floor function is instrumental in defining segment endpoints as (x, x Р2).
Step 1: Understanding Step Graphs
A step graph is characterized by its horizontal segments, where each segment is precisely 1 unit long. The left end of each segment is marked by a closed circle, which indicates that endpoint is included, while the right end has an open circle, signifying that endpoint is not included. This creates a visual representation that mimics steps in a staircase when plotted on a coordinate plane.
Step 2: Graphing the Segments
The initial segment of the step graph starts from the point (–3, –5) and extends to (–2, –5). Subsequently, every following segment moves 1 unit up along the y-axis and 1 unit to the right on the x-axis. As a result, this systematic pattern allows you to create multiple segments, gradually increasing in height, up until the final segment which concludes at (5, 2).
Step 3: Applying the Floor Function
The floor function contributes greatly to the layout of the step graph. It ensures that each segment’s left endpoint, represented by a closed circle, has coordinates expressed as (x, x – 2). Consequently, the way the segments are displayed means that the only option that matches this condition correctly will be the third choice among the alternatives provided. This illustrates how step graphs can effectively represent mathematical functions visually.