Answer :
Sure, let's go through the process of understanding 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 (F) to degrees Celsius (C).
2. Components of the Function: The formula [tex]\(\frac{5}{9}(F-32)\)[/tex] is derived from the relationship between the two temperature scales:
- The term [tex]\( F - 32 \)[/tex] adjusts the Fahrenheit value by the freezing point difference between the two scales.
- The multiplication by [tex]\(\frac{5}{9}\)[/tex] converts the value into Celsius, aligning with the difference in increments between the two scales (Fahrenheit has a 180-degree spread between freezing and boiling points of water, while Celsius has 100).
3. Interpreting [tex]\( C(F) \)[/tex]: In this context:
- [tex]\( C(F) \)[/tex] denotes the temperature in degrees Celsius.
- [tex]\( F \)[/tex] is the input variable that stands for the temperature in degrees Fahrenheit.
Thus, [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. This choice corresponds to the conversion process described, making it the correct interpretation of what [tex]\( C(F) \)[/tex] represents.
1. Understanding the Function: The function [tex]\( C(F) \)[/tex] is used to convert temperatures from degrees Fahrenheit (F) to degrees Celsius (C).
2. Components of the Function: The formula [tex]\(\frac{5}{9}(F-32)\)[/tex] is derived from the relationship between the two temperature scales:
- The term [tex]\( F - 32 \)[/tex] adjusts the Fahrenheit value by the freezing point difference between the two scales.
- The multiplication by [tex]\(\frac{5}{9}\)[/tex] converts the value into Celsius, aligning with the difference in increments between the two scales (Fahrenheit has a 180-degree spread between freezing and boiling points of water, while Celsius has 100).
3. Interpreting [tex]\( C(F) \)[/tex]: In this context:
- [tex]\( C(F) \)[/tex] denotes the temperature in degrees Celsius.
- [tex]\( F \)[/tex] is the input variable that stands for the temperature in degrees Fahrenheit.
Thus, [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. This choice corresponds to the conversion process described, making it the correct interpretation of what [tex]\( C(F) \)[/tex] represents.