What is a hyperbola and inverse variation?
In this post, we recognise that functions of the form f(x) = \frac{k}{x} represent inverse variation, identify the hyperbolic shape of their graphs and identify their asymptotes, as a part of the Prelim Maths Advanced course under the topic Working with Functions and sub-part Further Functions and Relations, specifically focusing on hyperbolas. An inverse variation is a relationship between two variables in which the product is a constant, so when one of the variables increases, the other will decrease proportionally so that the product is unchanged, the shape this relationship forms is a hyperbola.
Introduction to inverse variation
The following four videos will cover everything you need to know about inverse variations and how to solve the questions. The first and second video introduces some questions and guides you through how to solve them, while the third and fourth video goes over how to visually represent the hyperbola and graph it while understanding it’s properties.
Part 1: Quick Questions
Part 2: Painter Problem
Part 3: Thinking visually about the hyperbola
Part 4: Graphing principles
