Final answer:
The option that represents an exponential function is D: f(x) = (1/4)^-2x. An exponential function is defined as f(x) = b^x, where x is the exponent. Options A and C do not fit this definition, and B presents a base that is generally not considered in the definition of exponential functions in math.
Step-by-step explanation:
The question is asking which of the given functions is an exponential function. An exponential function is a mathematical function of the form f(x) = b^x, where b is the base and x is the exponent. Out of the options provided, option A: f(x) = 10^4+3x and option B: f(x) = (-5)^x resemble exponential functions. However, note that:
- Option A is not an exponential function because the exponent should depend solely on x; the term 10^4 makes it not purely exponential.
- Option B could be considered an exponential function in general terms; however, the base of an exponential function is typically a positive number.
- Option C: f(x) = (1/x)^6 is not an exponential function because it is a reciprocal raised to a power, not a base raised to the variable.
- Option D: f(x) = (1/4)^-2x is an exponential function because the variable x is found in the exponent.
While options A, B, and D could be confused as exponential, the most accurate and common definition of an exponential function is best represented by option D: f(x) = (1/4)^-2x, which is a true exponential function in mathematical terms.