Question

An exponential function is graphed for all real numbers. This includes which of the following sets of numbers?

Answer 1

In addition to linear, quadratic, rational, and radical functions, there are exponential functions. Exponential functions have the form f(x) = bx, where b > 0 and b ≠ 1. Just as in any exponential expression, b is called the base and x is called the exponent.

 

An example of an exponential function is the growth of bacteria. Some bacteria double every hour. If you start with 1 bacterium and it doubles every hour, you will have 2x bacteria after x hours. This can be written as f(x) = 2x.

 

Before you start,   f(0) = 20 = 1

After 1 hour           f(1) = 21 = 2

In 2 hours              f(2) = 22 = 4

In 3 hours              f(3) = 23 = 8

and so on.

 

 

With the definition f(x) = bx and the restrictions that b > 0 and that b ≠ 1, the domain of an exponential function is the set of all real numbers. The range is the set of all positive real numbers. The following graph shows f(x) = 2x.