Question

At a grocery store, almonds cost $5.99 per pound. In a relation, the input is the number of pounds of almonds, and the output is the cost. Is this relation a function? Why or why not?

A. Yes, because one input (number of pounds of almonds) will always have the same output (cost).
B. No, because almonds always cost $5.99 per pound.
C. No, because different inputs (numbers of pounds of almonds) will have different outputs (costs).
D. Yes, because almonds can cost different amounts.

Answer 1

The relationship between pounds of almonds and cost is a function because every input (number of pounds) corresponds to one specific output (cost), making answer (A) the correct choice.

Step-by-step explanation:

The situation described in the question presents a scenario where the cost of almonds is directly proportional to the weight purchased. The relationship between the number of pounds of almonds (the input) and the cost (the output) can be considered as a function because for each specific quantity of almonds, there is a corresponding cost. This consistency makes the relation a function, as every input has a unique and predictable output.

Answer (A) is the correct choice because it explains that the input (in this case, the number of pounds of almonds) will always have the same output (the cost) when multiplied by the per-pound price. This means that the relation is indeed a function according to the definition of a mathematical function, which states that each input should have exactly one output.