Final answer:
The best model for the relationship between the sales of sweaters (Y) and gloves (X) would be a linear function. Option (a) A linear function with a positive slope fits if there is a direct relationship where increases in X correspond to increases in Y. Option (d) A linear function with a negative slope applies if the relationship is inverse, with increases in X corresponding to decreases in Y.
Step-by-step explanation:
To determine which type of function best models the relationship between the sales of sweaters (Y) and gloves (X), we should consider the nature of the relationship. If the sales of sweaters and gloves tend to increase or decrease together, this suggests a positive relationship. A linear function is often used to model a direct relationship between two variables. Given that with a positive slope, as X increases, Y also increases and vice versa, option (a) A linear function with a positive slope would likely be a good fit if this direct relationship is consistent and can be drawn as a straight line.
However, if Ms. Clint has noticed that the sales of sweaters tend to go down as glove sales go up, or the other way around, this would suggest a negative relationship. In such a case, option (d) A linear function with a negative slope would be more appropriate, considering that a negative slope indicates an inverse relationship between two variables.
Other types of functions like quadratic or square root functions are used for different kinds of relationships, not typically for directly proportional or inversely proportional relationships like the one potentially described here. Without additional context indicating a more complex relationship, options (b) and (c) would be less likely to be correct.