Exponential and Logarithmic Functions: Comparing Logarithmic and Exponential Functions

Exponential Functions

f of x equals b to the x power with an arrow pointing to the b which is the base and an arrow pointing to the x which is the exponent.

The function f(x) = b^x is an exponential function with base b, where b is a positive real number other than 1, and x, the exponent, is any real number.

The following is a list of some exponential functions:

f(x) = 2^x
f(x) = 3^x
f(x) = 4^x

The following is the graph of f(x) = 2^x.

Graph of f of x equal to two to the x power.
f(x) = 2^x

Notice the asymptote of this graph is the x-axis or y = 0. The graph will approach the x-axis but will never touch it. We will discuss these graphs in more detail in the next section.