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The exponential function
A description of how we denote functions.
Surfaces as graphs of functions
Illustration of how the graph of a scalar-valued function of two variables is a surface.
Domain of functions
How to determine the domain of a function.
Limits of exponential functions at infinity
Calculating limits of exponential functions as a variable goes to infinity.
Exponential growth and decay: a differential equation
Solving a differential equation to find an unknown exponential function.
The function machine
The function machine metaphor helps explain the definition and properties of a function.
Basic examples of functions illustrating the definition of a function.
Function machine parameters
Illustrating function parameters as dials that influence the behavior of a function machine.
Function machine composition
Composing two functions simply means connecting together their respective function machines.
The function machine inverse
The inverse of a function is represented by running its function machine backwards.
Function composition examples
Examples of composing functions to form a new combined function.
Inverse function examples
Examples of forming an inverse function that does undoes the action of another function.
Exponential growth and decay modeled by discrete dynamical systems
Overview of exponential growth and decay in discrete time. Exploration of their qualitative properties as well as solutions to the dynamical system.
Discrete exponential growth and decay exercises
Exercises on solving problems involving exponential growth and decay in discrete time.
Discrete exponential growth and decay exercise answers
Answers to selected exercises on solving problems involving exponential growth and decay in discrete time.
Basic rules for exponentiation
A brief overview of the basic rules for exponents or powers.
Redundant parameters in the exponential function
Calculation showing that in the exponential function, changing either the base or a constant in the exponent have the same effect on the function.
The linear function
Overview of the linear function of one variable and a few of its properties.
Exploring the derivative of the exponential function
A guided tour into the reasons that the derivative of the exponential function with base e is the function itself.
How composing two functions forms a new combined function.
The exponential function