Identifying the Constant Function: Graph Interpretation Challenge

To solve this problem, we'll conduct the following steps:

• Step 1: Identify the vertex of the graph shown.
• Step 2: Compare the vertex to each function given in the choices.
• Step 3: Select the function whose vertex matches the graph.

Now, let’s work through these steps:

Step 1: The graph shows a vertex at the point (5, 0). This suggests that the graph is the absolute value function centered at $x = 5$.

Step 2: We compare this with each available function:
- $|x-5|$: This corresponds to a vertex at $(5, 0)$.
- $|x-3|$ would give a vertex at $(3, 0)$.
- $|x|$ would give a vertex at $(0, 0)$.
- $|5x|$ involves a similar transformation but with varied scaling and zero vertex.

Step 3: Therefore, the function $|x-5|$ perfectly matches the vertex (5, 0) of the graph plotted.

Our analysis confirms that the absolute value function corresponding to the graph is $|x-5|$.