What type of function is defined by the equation f(x) = ab^x?

The function defined by the equation ( f(x) = ab^x ) is characterized as an exponential function due to its unique form, where a constant ( a ) is multiplied by a base ( b ) raised to the power of the variable ( x ).

In exponential functions, the variable is in the exponent, which distinctly differentiates them from linear (constant rate of change) and quadratic functions (involving the square of the variable). The base ( b ) can affect the growth rate of the function. If ( b > 1 ), the function represents exponential growth, while ( 0 < b < 1 ) reflects exponential decay, clearly illustrating the rapid changes in the output values for small variations in ( x ).

This form also leads to unique graphical properties, where exponential functions exhibit a curve that continuously rises or falls rather than the straight lines of linear functions or the parabolic shapes of quadratic functions. The polynomial function is defined by a sum of powers of the variable with non-negative integer exponents and does not include base exponentiation involving a variable.

Thus, the defining characteristic of the equation ( f(x) = ab^x ) is that it is an exponential function, making the