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.

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 y-intercept of its graph.

Polynomial functions

Polynomial functions. Many common functions are polynomial functions. This unit describes polynomial functions and looks at some of their properties.

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.

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.

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.

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.

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.