Functions

Function is a mathematiical object in mathematics. In Calculus, we study properties of  functions. We will define basic concept of a function and related terminology such as domain, codomain and range.  Students will be introduced to piecewisely defined functions.

Syllabus

• Concept of a function, domain, codomain. The definition of the range of a function as the set of all possible images.
• Algebraic operations of functions: addition, substraction, multiplication, division.
• Examples of  functions: polynomials, rational functions, trigonometric functions.
• Piecewisely defined functions include greatest integer value function and absolute value function..
• Composition. Decomposition of a functions as composites of simpler functions.
• One-to-one functions and its inverse function. Increasing and decreasing functions and one-to-one functions.

Learning Objectives
 

• Students should be able to demonstrate their understanding of definition of function by being able to give examples of functions, check whether some given expression defines a function. The understanding of a function include being able to tell the domain, and codomain of a a given function. Besides, for some functions, students should be able to state the range  by verification via  definition.
• Apart from the known functions such as polynomials, and trigonometric functions first met in A-levels mathematics,  students should know of functions defined piecewisely, and functions such as greatest integer value function and absolute value function.
• Students should be able to determine the domain of combination (such as composition or quotient) of some functions and expressing the resulting function.
• Stdents should know how to verify that a function is one-to-one, and be aware of functions which are not one-to-one.
• Students should be able to find the inverse of a bijective function.

Reference: NG TB, Calculus, Chapter 2.