How long one can hold their breath can be calculated using the formula y=1.4g where y is the amount of time one can hold their breath in seconds and g is the size of their lungs in cubic centimeters.
Is this a relation or a function? Explain why.
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To determine whether the given equation represents a relation or a function, we need to understand the definitions of both terms.
A relation is a set of ordered pairs, where each input value is associated with one or more output values. In other words, it is a collection of input-output pairs.
A function, on the other hand, is a special type of relation where each input value is associated with only one output value. In a function, for every input, there is exactly one unique output.
In the given equation, y = 1.4g, where y represents the amount of time one can hold their breath in seconds and g represents the size of their lungs in cubic centimeters.
Here, for every value of g, we have a corresponding value of y. In other words, for a particular lung size (g), we can determine the specific time one can hold their breath (y). This implies that each input (g) yields a unique output (y).
Therefore, the given equation y = 1.4g represents a function since it satisfies the criteria of having a single output for each input.