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 :

Certainly! Let's break down the problem and understand what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] represents.

1. Understanding the Function:
- The function [tex]\( C(F) \)[/tex] is used to convert temperatures from degrees Fahrenheit to degrees Celsius.
- The variable [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.
- The expression [tex]\( \frac{5}{9}(F - 32) \)[/tex] is the formula used to find the equivalent temperature in degrees Celsius.

2. Components of the Function:
- The formula [tex]\( \frac{5}{9}(F - 32) \)[/tex] contains:
- The part [tex]\( F - 32 \)[/tex]: This adjusts the Fahrenheit temperature by 32, which is the offset based on the freezing point of water in Fahrenheit.
- The fraction [tex]\(\frac{5}{9}\)[/tex]: This is used to scale the temperature change from Fahrenheit to Celsius.

3. Role of [tex]\( C(F) \)[/tex]:
- [tex]\( C(F) \)[/tex] represents the output of the function, which is the temperature in degrees Celsius.
- Essentially, for a given temperature [tex]\( F \)[/tex] in degrees Fahrenheit, you input this into the function, and [tex]\( C(F) \)[/tex] gives you the corresponding temperature in degrees Celsius.

4. Conclusion:
- Therefore, [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.

So the correct description 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.