Which model represents a function?

A model that represents a function must adhere to the definition of a mathematical function: a relationship between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Here's a simple step-by-step approach to determine if a model represents a function:

1. Identify the inputs and outputs of the model. 2. Check if each input has only one output. This is often referred to as the vertical line test in the context of graphical models.

If you're dealing with a graphical model: - Draw vertical lines through the graph. - If any vertical line crosses the graph more than once, then the model does not represent a function because an input (represented by x-value) relates to more than one output (y-value).

If the model is a set of ordered pairs: - Look for repeated x-values with different y-values. - If you find any, the model does not represent a function.

If the model is a mathematical equation: - Solve the equation for y in terms of x (if possible). - If you can express y as a function of x without ambiguity, the model represents a function.

If the model is described in words: - Translate the description into an effective rule or mapping. - Determine if each input mentioned in the description maps to exactly one output.