Inverse variation

Definition

Inverse variation occurs when one variable increases while the other decreases, following the form $y = \frac{k}{x}$ where $k$ is a constant. This relationship creates a hyperbolic graph.

5 Must Know Facts For Your Next Test

1. In inverse variation, as one variable doubles, the other variable is halved.
2. The product of the two variables in an inverse variation is always constant ($xy = k$).
3. If a dataset follows inverse variation, its graph will be a hyperbola.
4. An example of inverse variation in real life is the relationship between speed and time for a constant distance.
5. To solve inverse variation problems, knowledge of rational functions and their properties is essential.

Review Questions

• What happens to one variable in an inverse variation if the other variable triples?
• How can you determine if a set of data points follow an inverse variation?
• What shape does the graph of an inverse variation take?

Related terms

Direct Variation: A relationship between two variables where they increase or decrease together, following the form $y = kx$.

Rational Function: A function that can be expressed as the ratio of two polynomials.

Hyperbola: A type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it appears as solutions.