The introduction to mathematical functions covers basic definitions, ordered pairs, their equality, and initial examples.

• Basic definitions such as ordered pairs and their components are reviewed.
• Equality of ordered pairs is explained with examples.
• An exercise is given to practice the definition of ordered pair equality.

The Cartesian product of sets and its properties are explained with diagrams and examples.

• The Cartesian product is defined with examples using set diagrams and tree diagrams.
• Properties of the Cartesian product, such as non-commutativity and extension to more than two sets, are discussed.
• Examples are given to show how to calculate the number of elements in a Cartesian product.

The concepts of domain and range of relations are introduced with definitions and graphical illustrations.

• Domain and range are defined for relations with visual examples.
• The distinction between domain and range is illustrated with a graph of two sets, A and B.
• Graphical representation of the Cartesian product is used to explain domain and range.

Different types of relations are explained, including reflexive, symmetric, transitive, and equivalence relations.

• Reflexive, symmetric, and transitive properties of relations are defined.
• A relation that satisfies all three properties is named an equivalence relation.
• Examples are provided to illustrate these types of relations.

Special functions and their graphical representations are covered, including constant, identity, absolute value, and more.

• Special functions such as constant, identity, absolute value, sign, square root, cubic, step, quadratic, multiplicative inverse, and floor functions are introduced.
• Graphical representations of these functions are shown, with explanations on how to sketch their graphs.
• Domain and range for each special function are explained.