Short Answer 
The characteristics of the logarithmic graph indicate that it behaves as a function with a base greater than 1, specifically deduced to be 6. The points on the graph have been verified against the function y = log‚ÄöCU(x), confirming that this is the correct representation of the graph’s behavior.
Step 1: Identify the Characteristics of the Graph
To determine the function of the logarithmic graph, first, observe the general behavior of the curve. In this case, the y-values increase as the x-values increase, indicating that we are dealing with a logarithmic function where the base is greater than 1. Key points to note include:
- The graph starts in Quadrant 4 and moves towards Quadrant 1.
- Points given on the graph include: (0.5, -0.4), (1, 0), and (6, 1).
Step 2: Analyze the Given Points and Function Options
The next step is to analyze the given points against the function options. From the points, we can see that as x values increase, the y values also increase. This implies that the base of the logarithm, b, must be greater than 1. The relevant function options include:
- y = log(1/6) x
- y = log(0.5) x
- y = log(1) x
- y = log(6) x
Step 3: Verify the Chosen Function with Given Points
After deducing that b must be 6 based on the clues from point values, verify by substituting the points into the equation y = log‚ÄöCU(x). You can check various coordinates:
- At x = 0.5: 6^(-0.4) ‚Äöaa 0.488, which is close to the point (0.5, -0.4).
- At x = 1: 6^0 = 1, confirming that (1, 0) is part of the graph.
- At x = 6: 6^1 = 6, confirming that (6, 1) is also part of the graph.
Thus, the function of the graph is ultimately determined to be: y = log‚ÄöCU(x).