To determine the logarithmic function that represents the data in the table, we first need to analyze the provided values:
- x: 1, fx: 0
- x: 3, fx: 1
- x: 9, fx: 2
Noting that the fx values might correspond to the logarithm of the x values, we can express the relationship between x and fx as:
fx = log_b(x),
where b is the base of the logarithmic function.
From the data, we can observe:
- When x = 1, fx = log_b(1) = 0 (true for any base b)
- When x = 3, we need to find b such that log_b(3) = 1. This implies b = 3.
- When x = 9, we need log_b(9) = 2, which also verifies if the base is 3, since 9 is equal to 32.
Therefore, the logarithmic function that fits the provided data points is:
fx = log3(x)
This function implies that as x increases, fx increases as well, preserving the logarithmic nature of the correlation laid out by the points in the table. The vertical scale in the function corresponds directly to the logarithmic increase represented by the table data.