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Which statement best justifies whether or not the relationship between the length and price represents a function?

A. This relationship does not represent a function because the prices of different lengths of ribbon are all different.
B. This relationship represents a function because no length of ribbon has more than one price.
C. This relationship does not represent a function because it relates inches and dollars.
D. This relationship represents a function because the price per inch decreases as the length of ribbon increases.

1 Answer

2 votes

Final answer:

The correct justification for the relationship between length and price being a function is option B, which states that each length of ribbon has only one price, therefore satisfying the definition of a function. The relationship's linearity and the correlation coefficient do not determine its qualification as a function.

Step-by-step explanation:

The statement that best justifies whether or not the relationship between the length and price represents a function is: B. This relationship represents a function because no length of ribbon has more than one price. A function is defined in mathematics as a relationship where each input (in this case, the length of ribbon) is associated with exactly one output (the price of the ribbon). Since each length has a unique price and doesn't vary, this scenario defines a functional relationship between length and price.

It's also essential to understand that a function doesn't require a linear relationship or a direct proportion between variables, as indicated by statements suggesting the relationship doesn't seem to be linear. The significant correlation coefficient (r = .8944) implies a strong association between length and price, yet this doesn't invalidate the definition of a function, as long as the one-to-one relationship is maintained.

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