Funktionsbegriff: Was ist eine Funktion?

Understanding Functions in Mathematics

Definition of a Function

• The concept of functions is introduced, emphasizing the importance of understanding this term for future assessments.

• A function is defined as a unique assignment where each input (x-value) corresponds to exactly one output (y-value).

Testing for Functions

• To determine if a relation is a function, one can use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

• An example illustrates that for x = -3 and 0, there is only one intersection point with the y-axis, confirming it as a function.

Identifying Non-functions

• Continuing with examples, when testing values between intersections shows multiple y-values for an x-value (e.g., x = -1), it indicates that the relation does not represent a function.

• A visual representation demonstrates how certain areas yield multiple intersection points, leading to ambiguity in y-values associated with specific x-values.

Conclusion on Function Characteristics

• The discussion highlights that having more than one y-value for any given x-value disqualifies the relation from being classified as a function.