Exponential Functions

Exponential Functions: A function where the base is a real number greater than zero, excluding one,
and the power is a variable. The variable is any real number and the base cannot equal one.

Correct Form

Incorrect Form

Polynomials often times get mixed up with exponential functions. Polynomials have the variable as the base while exponential functions have the variable as the power.

If the variable is negative then you take the function and place it in the denominator under one. 

Exponential Functions have a horizontal asymptote at Y=0 and the domain is always All Real Numbers. The graphs of exponential functions can be altered.

By adding D to the exponential function the graph will be shifted vertically

By multiplying A to the exponential function the graph will either be vertically stretched or compressed. If A is negative then the graph will be reflected over the X-axis.

By subtracting or adding C the graph will be shifted either right or left. 

By changing the base the graph will become either more or less aggressive. The larger the base the faster the graph will grow. When B is less than one the graph decays.  

The graph has moved five units upwards because five was added to the base. This created a new horizontal asymptote at Y=5. The graph was vertically stretched because the base was multiplied by five.