Which of the following is the form of an exponential function?

• A. f(x) = ax + b
• B. f(x) = a + b^x
• C. f(x) = x^2
• D. f(x) = ab^x

Answer: (D)

Exponential functions have the variable in the exponent. The form ab^x fits this perfectly: x sits in the exponent while a is a constant that scales the whole function and b is the base that controls growth or decay. In a linear function, x appears to the first power (ax + b), and in a polynomial like x^2, x is not in the exponent at all. The expression a + b^x does place x in the exponent, but the presence of the extra constant term a outside the exponential means it isn’t the standard exponential form used to describe growth or decay patterns. So ab^x is the form that clearly shows the variable as an exponent and aligns with the typical exponential function.