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Convert temperature from Celsius to Fahrenheit

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In the real world, what might be a situation where it is preferable for the data to form a relation but not a function?

There is a formula that converts temperature in degrees Celsius to temperature in degrees Fahrenheit. You are given the following data points:

Fahrenheit Celsius
Freezing point of water 32 0
Boiling point of water 212 100

1. Find the linear equation that expresses temperature in degrees Fahrenheit as a function of temperature in degrees Celsius.

2. Find the linear equation that expresses temperature in degrees Celsius as a function of temperature in degrees Fahrenheit.

3. How do the graphs of these two functions differ?
Do not just list the functions. You must show all of the steps you used to derive the functions.

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Solution Preview

Please see the attached file.

First of all, let us define a function: A function is a relation where no x -value appears more than once (with different y-values).
A one-to-one function is a function where each x -value corresponds to only one y-value.
A regular function can occur when one y-value correspond to 2 x-values.

There is an easy way to remember this:

Let us say that the data represented by x values is kids (John, Rick, Bill, Tom)
And the one that is represented by y-values is mothers ( Mary, Sue, Anne)
(Domain) (Range)
Kids Mothers
John Mary

Rick Sue

Bill Anne

Tom Lina

As you can see, John CANNOT have 2 mothers, but Anne CAN have 2 kids.

Of course, a One-to-One function occurs when Each Mother has ONLY ONE kid.

In the real ...

Solution Summary

The solution includes a word document with a step by step solution to find the formula that converts temperature from Celsius to Fahrenheit. It also includes a full explanation on the concept of functions.