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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 the question, we need to understand what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is doing.

1. Identify the Inputs and Outputs of the Function:
- In this function, [tex]\( F \)[/tex] is the input. It represents the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the output. It represents the temperature that's been converted into degrees Celsius.

2. Understand the Conversion Formula:
- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is used to convert a temperature from Fahrenheit to Celsius. This is a common formula used in weather calculations.

3. Translate the Function into Words:
- The function takes a temperature value in Fahrenheit as input.
- It performs the mathematical operation to convert this temperature to Celsius.
- The result, [tex]\( C(F) \)[/tex], is the temperature in degrees Celsius.

4. Select the Correct Description:
- Based on the above understanding, the correct description of [tex]\( C(F) \)[/tex] 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."

Thus, the correct interpretation of [tex]\( C(F) \)[/tex] in the context of the given function is 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."

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