High School

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, let's break down the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].

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

2. Looking at the Options:
- First Option: "C(F) represents the output of the function C in degrees Celsius when the input F is in degrees Fahrenheit."
- This is accurate because the function [tex]\( C \)[/tex] converts a given temperature [tex]\( F \)[/tex] (in Fahrenheit) into [tex]\( C(F) \)[/tex] (in Celsius).

- Second Option: "C(F) represents the output of the function F in degrees Fahrenheit when the input C is in degrees Celsius."
- This is incorrect because it speaks of a function [tex]\( F \)[/tex], which is not defined in this context, and it reverses the roles of Fahrenheit and Celsius.

- Third Option: "C(F) represents the output of the function C in degrees Fahrenheit when the input F is in degrees Celsius."
- This is incorrect because the output [tex]\( C(F) \)[/tex] is in degrees Celsius, not Fahrenheit.

- Fourth Option: "C(F) represents the output of the function F in degrees Celsius when the input C is in degrees Fahrenheit."
- This is incorrect for similar reasons as the second option; it reverses the roles and mislabels the units.

3. Conclusion:
- The correct interpretation is: "C(F) represents the output of the function C in degrees Celsius when the input F is in degrees Fahrenheit."

This means that [tex]\( C(F) \)[/tex] provides the temperature in degrees Celsius corresponding to the given temperature [tex]\( F \)[/tex] in degrees Fahrenheit.