Question

 

Determine if the function f is an exponential function. If so, identify the base. If not, why not? f(x) = 22x

 

Answer 1

The function

From the basic laws of exponents (a^x )^y = a^xy

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.

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.

Therefore is exponetial function.

Base of the exponential function is 4.

Answer 2

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.

The function is f(x) = 2^2x.

Apply Power of a power property : a^mn = (a^m)ⁿ.

f(x) = 2^2x = (2²)^x = 4^x.

The above function represents exponential function, since the base 4 is greater than zero.