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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 :

Sure! Let's break down the problem step by step.

Siera wants to convert a temperature from degrees Fahrenheit to degrees Celsius using the function:

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

Here's what each part of the function represents:

- [tex]\(C(F)\)[/tex]: This is the output of the function. It represents the temperature in degrees Celsius after the conversion.
- [tex]\(F\)[/tex]: This is the input to the function, representing the temperature in degrees Fahrenheit.

The formula itself, [tex]\(\frac{5}{9}(F - 32)\)[/tex], is the standard formula for converting temperatures from Fahrenheit to Celsius. It takes the temperature in Fahrenheit ([tex]\(F\)[/tex]), subtracts 32, and then multiplies the result by [tex]\(\frac{5}{9}\)[/tex].

The options given are:

1. [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.

2. [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.

3. [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.

4. [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.

Based on the explanation above, the correct interpretation 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.

Therefore, the correct choice is the first option. This explanation describes accurately what the function does when you use it to convert temperatures from Fahrenheit to Celsius.

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