Final answer:
The set of ordered pairs (3,5), (2,5), (5,8), (3,1) is not a function because the input '3' maps to two different outputs, violating the definition of a function, which requires each input to map to exactly one output.
Step-by-step explanation:
To determine if a set of ordered pairs is a function or just a relationship, we must assess whether each input (the first number in each ordered pair, which represents the independent variable) maps to exactly one output (the second number in the ordered pair, which represents the dependent variable). The set of ordered pairs given: (3,5), (2,5), (5,8), (3,1) includes two pairs with the same first number but different second numbers: (3,5) and (3,1). This indicates that the input '3' maps to two different outputs, '5' and '1'. Consequently, this set does not represent a function but is merely a relationship because a function by definition would have each input related to one and only one output.
A way to practically assess the dependence of y on x is to visualize these pairs on a graph. If you could draw a vertical line that intersects the graph at more than one point, then by the vertical line test, it is not a function. Professionals use mathematical functions to describe the relationship between variables, which is essential in the fields such as economics, physics, and biology.