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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 understand what [tex]\( C(F) \)[/tex] represents, we need to look at the function provided:

[tex]\[ C(F) = \frac{5}{9}(F-32) \][/tex]

This function is used to convert temperatures from degrees Fahrenheit ([tex]\( F \)[/tex]) to degrees Celsius ([tex]\( C \)[/tex]). Let's break down the components:

1. Input Variable: The variable [tex]\( F \)[/tex] is the input of the function, which represents the temperature in degrees Fahrenheit.

2. Function Process: The formula [tex]\(\frac{5}{9}(F-32)\)[/tex] is the mathematical operation used to convert the Fahrenheit temperature to Celsius.

3. Output Variable: The result of the function, [tex]\( C(F) \)[/tex], is the temperature in degrees Celsius.

Based on this understanding, [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. Therefore, [tex]\( C(F) \)[/tex] corresponds to the conversion from Fahrenheit to Celsius.

So, the correct choice is:

[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.

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