Answer :
To determine what [tex]$C(F)$[/tex] represents in the given function [tex]$C(F) = \frac{5}{9}(F-32)$[/tex], we need to understand what the function is doing:
1. Identify the Function's Purpose: The function [tex]$C(F)$[/tex] is a mathematical formula used to convert temperatures from degrees Fahrenheit (F) to degrees Celsius (C).
2. Function Structure: In the formula [tex]$C(F) = \frac{5}{9}(F - 32)$[/tex]:
- [tex]$F$[/tex] is the input of the function, which is the temperature in degrees Fahrenheit.
- The expression [tex]\((F - 32)\)[/tex] is used to adjust for the difference between the Fahrenheit and Celsius scales at the freezing point of water.
- The fraction [tex]\(\frac{5}{9}\)[/tex] is used to scale the difference according to the conversion factor between the Fahrenheit and Celsius scales.
3. Interpret the Output: The result of the function, [tex]$C(F)$[/tex], gives the equivalent temperature in degrees Celsius after converting from degrees Fahrenheit.
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. This matches the first option presented in the question.
1. Identify the Function's Purpose: The function [tex]$C(F)$[/tex] is a mathematical formula used to convert temperatures from degrees Fahrenheit (F) to degrees Celsius (C).
2. Function Structure: In the formula [tex]$C(F) = \frac{5}{9}(F - 32)$[/tex]:
- [tex]$F$[/tex] is the input of the function, which is the temperature in degrees Fahrenheit.
- The expression [tex]\((F - 32)\)[/tex] is used to adjust for the difference between the Fahrenheit and Celsius scales at the freezing point of water.
- The fraction [tex]\(\frac{5}{9}\)[/tex] is used to scale the difference according to the conversion factor between the Fahrenheit and Celsius scales.
3. Interpret the Output: The result of the function, [tex]$C(F)$[/tex], gives the equivalent temperature in degrees Celsius after converting from degrees Fahrenheit.
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. This matches the first option presented in the question.