Definition: In an antiproportional relationship, as one quantity increases, the other quantity decreases proportionally, maintaining a constant product.

Example: Distribution of gummy bears among people - as the number of people increases, the number of gummy bears per person decreases proportionally.

Highlight: The graph of an antiproportionale funktion forms a hyperbola that never touches the coordinate axes.

Vocabulary: A hyperbola is the mathematical term for the curved graph representing an antiproportional relationship.

Definition: In a proportional relationship, as one quantity increases, the other quantity increases proportionally.

Example: A pricing example where 1kg of pasta costs €10, so 10kg would cost €100, demonstrating dreisatz beispiele in practice.

Highlight: The graph of a proportional relationship is always a straight line passing through the origin (0,0).

Vocabulary: The proportionality factor $k$ is the constant ratio between corresponding values in a proportional relationship.