Functions and Graphs

Introduction to functions
Introduction to functions. A function is a rule which operates on one number to give another number. However, not every rule describes a valid function. This unit also introduces some of the mathematical terms associated with functions.Length: 32 minutes 
Linear functions
Linear functions. Some of the most important functions are linear. This unit describes how to recognize a linear function and how to find the slope and the yintercept of its graph.Length: 19 minutes 
Polynomial functions
Polynomial functions. Many common functions are polynomial functions. This unit describes polynomial functions and looks at some of their properties.Length: 43 minutes 
Exponential and logarithm functions
Exponential and logarithm functions. Exponential functions and logarithm functions are important in both theory and practice. In this unit the graphs of exponential and logarithm functions are examined and their relationships established.Length: 44 minutes 
Trigonometric functions
Trigonometric functions. The sine, cosine and tangent of an angle are all defined in terms of trigonometry, but they can also be expressed as functions. How to restrict the domain of each function in order to define an inverse function is also described.Length: 25 minutes 
Hyperbolic functions
Hyperbolic functions. The hyperbolic functions have similar names to the trigonometric functions, but they are defined in terms of the exponential function. This unit defines the three main hyperbolic functions and sketches their graphs. Inverse functions and reciprocal functions are also considered.Length: 29 minutes 
Composition of functions
Composition of functions. Complicated functions can be built up from simple functions by using the process of composition, where the output of one function becomes the input of another. It is also sometimes necessary to decompose a function into two simpler functions.Length: 11 minutes 
Inverse functions
Inverse functions. An inverse function is a second function which undoes the work of the first one. In this unit two methods for finding inverse functions are described, together with the possible need to restrict the domain of a function before an inverse function can exist.Length: 18 minutes