1. GRAPHS OF LOGARITHMIC AND EXPONENTIAL FUNCTIONS

2. Graphs of Exponential Functions  Exponential functions are functions based on the function y = b x.  These functions’ graphs exist for all x.  As x increases, y increases more and more quickly.  As x decreases, y approaches 0.  As with other kinds of functions, exponential functions can be translated, reflected, and dilated in the usual ways.

3. Exponential Functions: Example This is a graph of y = e x, an exponential function that you will probably see and use relatively often.

4. Graphs of Logarithmic Functions  Logarithmic functions are functions based on the function y = log b (x).  These functions’ graphs exist for all x > 0.  As x increases, y increases, although its rate of increase greatly slows.  As x approaches 0, y decreases without bound.  Again, logarithmic functions can be translated, reflected, and dilated.

5. Logarithmic Functions: Example This is a graph of y = ln(x), a logarithmic function that you will probably see and use relatively often.

6. Exponential and Logarithmic Functions  Exponential functions and logarithmic functions are inverses of each other.  This means that if you have an exponential function f(x) = b x and a logarithmic function g(x) = log b (x), f(g(x)) = x and g(f(x)) = x.  This also means that the graphs of b x and log b (x) are reflections of one another over the line y = x.

7. Graph Here, y = e x and y = ln(x) are graphed on the same axes, along with the line y = x. As you can see, the two are reflections of one another across this line.