General Mathematics - Functions and their Graphs

Introduction to Relations and Functions00:00:01

The lesson introduces basic definitions: relations as sets of ordered pairs, domain as the set of x-values (input), and range as the set of y-values (output). A function is defined as a relation where every domain value maps to exactly one range value.

Linear Functions00:06:40

Explanation of linear functions using the slope-intercept form (y = mx + b). It details how the slope (m) determines the line's tilt and how to sketch these graphs by identifying x and y intercepts.

Application of Linear Functions00:18:01

A practical example using a taxi fare calculation to demonstrate how linear equations model real-life scenarios, including fixed rates and variable costs.

Quadratic Functions00:27:06

Introduction to quadratic functions in general and vertex form. Concepts include the parabola shape, axis of symmetry, vertex identification, and using the discriminant to determine root existence.

Application of Quadratic Functions00:54:05

Real-world problem solving using quadratic functions, such as modeling a basketball's trajectory to find its maximum height and optimizing the area of a rectangular garden.