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For one month, Siera calculated her hometown's average high temperature in degrees Fahrenheit. She wants to convert that temperature from degrees Fahrenheit to degrees Celsius using the function [tex]C(F)=\frac{5}{9}(F-32)[/tex]. What does [tex]C(F)[/tex] represent?

A. [tex]C(F)[/tex] represents the output of the function [tex]C[/tex] in degrees Celsius when the input [tex]F[/tex] is in degrees Fahrenheit.

B. [tex]C(F)[/tex] represents the output of the function [tex]F[/tex] in degrees Fahrenheit when the input [tex]C[/tex] is in degrees Celsius.

C. [tex]C(F)[/tex] represents the output of the function [tex]C[/tex] in degrees Fahrenheit when the input [tex]F[/tex] is in degrees Celsius.

D. [tex]C(F)[/tex] represents the output of the function [tex]F[/tex] in degrees Celsius when the input [tex]C[/tex] is in degrees Fahrenheit.

Answer :

To solve this question, we need to understand what the function [tex]\( C(F) \)[/tex] represents in the context given.

1. Understanding the Function: The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is used to convert temperatures from degrees Fahrenheit to degrees Celsius.

2. Identifying the Input and Output:
- The input to this function is [tex]\( F \)[/tex], which represents the temperature in degrees Fahrenheit.
- The output is [tex]\( C(F) \)[/tex], which calculates the temperature in degrees Celsius.

3. Determining the Correct Interpretation:
- We know that the function is designed for converting Fahrenheit ([tex]\( F \)[/tex]) to Celsius ([tex]\( C \)[/tex]).
- Therefore, [tex]\( C(F) \)[/tex] must be the Celsius temperature corresponding to the given Fahrenheit temperature [tex]\( F \)[/tex].

Using this information, we conclude that:

[tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit.

This matches with the first option:
- [tex]$C(F)$[/tex] represents the output of the function [tex]$C$[/tex] in degrees Celsius when the input [tex]$F$[/tex] is in degrees Fahrenheit

Thus, the correct choice is the first statement.

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