Final answer:
A function is different from a relation because it assigns exactly one output to every input, whereas a relation could assign multiple outputs to a single input. Functions are essential in mathematical economic models, particularly in linear equations used to represent relationships between variables.
Step-by-step explanation:
The question Why is a function different from a relation? addresses a key concept in mathematics, specifically within algebra. To answer the question, a function is a type of relation but with a special condition: each input is related to exactly one output. This is what differentiates it from a general relation, where an input can be related to multiple outputs. In terms of mathematical economic models, functions are used to define relationships between variables, such as linear equations, which are a simple type of function. For instance, in a linear equation y = mx + b, for each value of x there is exactly one corresponding value of y, fitting the definition of a function.
An example using a linear equation in the context of statistical economic models is y = a + bx, where a is the y-intercept, and b is the slope or rate of change. Such functions help in delineating how one variable (dependent variable) changes with respect to the other (independent variable).
The correct answer to the original question is c) A function is a relation that assigns exactly one output to every input.