Determine if the function f is an exponential function If so

Determine if the function f is an exponential function. If so, identify the base. If not, why not?

f(x) = x^3.141

Solution

Definition of Exponential Function : The exponential function with base b is denoted by f( x ) = b^x, where b > 0, b 1, and x is any real number.

For example, f(x) = 3^x is an exponential function, and g(x) = ( 4/17)^x is an
exponential function.

An exponential function is a function of the form y = b^x. where b is a positive number not equal to 1, and x is any real number.

Thus, exponential functions have a constant base; the variable is in the exponent.

The number b is called the base of the exponential function.

But, The function p(x) = x^(-3.141) is a polynomial. Here the “variable”, x, is being raised to some constant power.

Therefore, given function is NOT exponentialfunction. but polymomial function.