What is Exponential Function Definition?

In mathematics, a function means a correspondence from one value x of the first set to another value y of the second set.

Answer: The exponential functions are the functions of the form f(x) = a^x

Here, a (≠ 0) is called the base, and x is known as the exponent.

Explanation:

The exponential functions are the functions of the form f(x) = a^x.

Here, f(x) is function of 'x', 'a' is any number, except 0. It is called the base.

'x' is the exponent. It can take values starting from 0. The exponent can also be called the 'index'.

If the value of base in an exponential function is greater than 1, then the function increases exponentially.

If the value of base in an exponential function is less than 1 but greater than 1, then the function decreases exponentially.

If the value of the base is 1, then the graph makes a line at y = 1 or y = a.

The exponent power can be positive or negative. 

If the rate of increase in a quantity is positive then it is called exponential growth. If the rate of increase is negative then it is called exponential decay.

Hence, the exponential functions are the functions of the form f(x) = a^x.