Answer :
To understand what [tex]$C(F)$[/tex] represents in the function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex], let's break down what each part of the function means:
1. Function Purpose: The function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] is used to convert temperatures from degrees Fahrenheit to degrees Celsius.
2. Input and Output:
- Input: The variable [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.
- Output: The function [tex]\( C(F) \)[/tex] gives us the temperature in degrees Celsius once we input a temperature in Fahrenheit.
3. Understanding the Conversion:
- The formula [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] derives from the relationship between the Celsius and Fahrenheit scales.
- Subtracting 32 from [tex]\( F \)[/tex] adjusts for the different zero points of the two scales.
- Multiplying by [tex]\(\frac{5}{9}\)[/tex] adjusts for the different sized intervals: there are 180 Fahrenheit degrees between the freezing and boiling points of water, compared to 100 Celsius degrees.
Given these details, let's precisely state what [tex]\( C(F) \)[/tex] represents:
- Correct Representation: [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 means for any specific value of [tex]\( F \)[/tex], the function outputs the corresponding temperature in Celsius, which matches the conversion function's main goal.
1. Function Purpose: The function [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] is used to convert temperatures from degrees Fahrenheit to degrees Celsius.
2. Input and Output:
- Input: The variable [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.
- Output: The function [tex]\( C(F) \)[/tex] gives us the temperature in degrees Celsius once we input a temperature in Fahrenheit.
3. Understanding the Conversion:
- The formula [tex]\( C(F) = \frac{5}{9}(F-32) \)[/tex] derives from the relationship between the Celsius and Fahrenheit scales.
- Subtracting 32 from [tex]\( F \)[/tex] adjusts for the different zero points of the two scales.
- Multiplying by [tex]\(\frac{5}{9}\)[/tex] adjusts for the different sized intervals: there are 180 Fahrenheit degrees between the freezing and boiling points of water, compared to 100 Celsius degrees.
Given these details, let's precisely state what [tex]\( C(F) \)[/tex] represents:
- Correct Representation: [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 means for any specific value of [tex]\( F \)[/tex], the function outputs the corresponding temperature in Celsius, which matches the conversion function's main goal.