Final answer:
When determining f(16) for various types of functions given two points, a linear function suggests f(16) should be 54, while the values for a power, exponential, and logarithmic function cannot be determined with the provided information alone.
Step-by-step explanation:
To infer the value of f(16), we must understand the nature of the function based on the given pairs (4, 6) and (8, 18).
Linear Function
For a linear function, we observe that when x doubles from 4 to 8, f(x) triples from 6 to 18. If this proportional change continues, when x doubles again from 8 to 16, f(x) should triple again from 18 to 54. Hence, f(16) = 54 in a linear pattern.
Power Function
In a power function, we expect changes in f(x) to follow a specific power of x. The relationship is not linear, so we cannot infer it directly without more information. Consequently, f(16) for a power function cannot be determined with the current data provided.
Exponential Function
In an exponential function, values typically increase by a factor related to the base of the exponent. The exponential growth pattern is not explicitly clear from two points, so we cannot determine f(16) without additional information.
Logarithmic Function
For a logarithmic function, values increase as the log of x. However, the relationship between the given input-output pairs does not suggest a clear logarithmic pattern, so f(16) is undetermined without extra information.