Exponential function is a function with a positive constant other than 1 raised to an exponent that includes a variable.
The basic form of the exponential function is f(x)=bx (b is the base and x is the exponent).
The base b is always positive (b>0) and not equal to one (b≠1).
For example: the function f(x)=3x is an exponential function where the base is a constant b=3 and the exponent is the variable x.
The y axis intercept of the basic exponential function graph f(x)=bx is equal to 1 for all values of b.
An exponential function slope is always increasing or always decreasing. The slope form depends on the value of the base b. All graphs of exponential functions are curved.
The ends of the exponential function graph: The graph of a basic exponential function f(x)=bx has a horizontal asymptote on one of its ends (positive x axis or negative x axis). The other end of the function approaches infinity. The end behavior depends on the value of the base b.
We can shift an exponential function graph by adding a constant to the function or by multiplying the exponential term by a coefficient, so that the basic function f(x)=bx will become f(x)=a*bx+d.
Continue reading this page for detailed explanations and examples.