QuestionLaurie's candy dispenser dispenses candy tripling for each pound per square inch of pressure. Is this a relation, function, both, or neither?
Studdy Solution
STEP 1
Assumptions1. The amount of candy dispensed is directly proportional to the pressure applied on the lever.
. For each pound per square inch of pressure placed on the lever, the amount of candy dispensed will triple.
3. We need to determine if this situation represents a relation, a function, neither, or both.
STEP 2
First, let's define what a relation and a function are in mathematics.
A relation is a set of ordered pairs. In this case, the pressure applied on the lever and the amount of candy dispensed can be considered as an ordered pair (pressure, candy).
A function is a special type of relation where each input (in this case, pressure) has exactly one output (in this case, candy).
STEP 3
In this situation, for each unique pressure applied to the lever, there is a unique amount of candy dispensed. This means that each input has exactly one output.
Therefore, this situation represents a function.
STEP 4
Since a function is a special type of relation, this situation also represents a relation.
Therefore, this situation represents both a relation and a function.
The correct answer is D. Both a relation and a function.
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