College

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][tex]$C(F)$[/tex][/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][tex]$C(F)$[/tex][/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][tex]$C(F)$[/tex][/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][tex]$C(F)$[/tex][/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 the context of the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].

1. Identify the Function's Purpose:
- The function [tex]\( C(F) \)[/tex] is designed to convert temperatures from degrees Fahrenheit to degrees Celsius.
- In this function:
- [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit (the input).
- [tex]\( C(F) \)[/tex] is the temperature in degrees Celsius (the output).

2. Understanding the Function Notation:
- In the notation [tex]\( C(F) \)[/tex], [tex]\( C \)[/tex] indicates that it is a function that calculates Celsius temperatures.
- The variable [tex]\( F \)[/tex] inside the parenthesis represents the input of the function, which is the temperature in Fahrenheit.

3. Interpret the Output:
- When you input a Fahrenheit temperature into the function [tex]\( C(F) \)[/tex], it processes this input and provides an output in degrees Celsius.
- Therefore, [tex]\( C(F) \)[/tex] gives the temperature in degrees Celsius corresponding to the provided Fahrenheit temperature.

4. Match with Given Options:
- Option 1: "C(F) represents the output of the function C in degrees Celsius when the input F is in degrees Fahrenheit."
- This option accurately describes the function: it converts a Fahrenheit temperature to a Celsius temperature.

- Option 2: "C(F) represents the output of the function F in degrees Fahrenheit when the input C is in degrees Celsius."
- Incorrect: This suggests the reverse process, a conversion from Celsius to Fahrenheit, which the given function does not do.

- Option 3: "C(F) represents the output of the function C in degrees Fahrenheit when the input F is in degrees Celsius."
- Incorrect: This suggests that the output is in Fahrenheit, which is not what the function does.

- Option 4: "C(F) represents the output of the function F in degrees Celsius when the input C is in degrees Fahrenheit."
- Incorrect: The function [tex]\( C \)[/tex] is not taking Celsius input nor is it outputting Fahrenheit.

Based on this analysis, the correct interpretation of what [tex]\( C(F) \)[/tex] represents is:

"C(F) represents the output of the function C in degrees Celsius when the input F is in degrees Fahrenheit."