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A $5,$10,$20,$50, or $100 bill is mapped to all the sets of coins that are the same as the total value of the bill. Tell whether this situation represents a function. Explain your reasoning. If the situation represents a function, give the domain and range.

User Oronbz
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4 votes

Answer:

This situation represents a function. The domain is {A, B, C, D, E} and the range is {$5, $10, $20, $50, $100}.

Explanation:

Firstly, we need to know what a function is:

It is simply something that relates an input to an output. Like for instance a mirror is a function that relates your face to your image. In lay terms we can call something a function if and only if it can relate one thing to another. Mathematically, a function is called a function if and only if every input has a distinct output, just as how one face can't produce two images at a time when looked at the mirror. The input is called the domain and output range.

Now, in the question we are told that all the bills are mapped – related in lay terms – to some set of coins that are exactly the same number of the bills. This means each bill has a distinct input. Here is a clearer picture:

A to 5 usd

B to 10usd

C to 20usd

D to 50usd

E to 100usd

Where A, B, C, D and E respectively stand for the distinct coins that are mapped to the distinct bill.

From here, each coin has it distinct output. Therefore it is a function.

The domain is {A, B, C, D, E} and the range is {$5, $10, $20, $50, $100}.

User Krishna Chaurasia
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