Answer :
To solve this question, we need to understand the context of the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
1. Identify the Function's Purpose:
- The function [tex]\( C(F) \)[/tex] is designed to convert temperatures from degrees Fahrenheit to degrees Celsius.
- In this function:
- [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit (the input).
- [tex]\( C(F) \)[/tex] is the temperature in degrees Celsius (the output).
2. Understanding the Function Notation:
- In the notation [tex]\( C(F) \)[/tex], [tex]\( C \)[/tex] indicates that it is a function that calculates Celsius temperatures.
- The variable [tex]\( F \)[/tex] inside the parenthesis represents the input of the function, which is the temperature in Fahrenheit.
3. Interpret the Output:
- When you input a Fahrenheit temperature into the function [tex]\( C(F) \)[/tex], it processes this input and provides an output in degrees Celsius.
- Therefore, [tex]\( C(F) \)[/tex] gives the temperature in degrees Celsius corresponding to the provided Fahrenheit temperature.
4. Match with Given Options:
- Option 1: "C(F) represents the output of the function C in degrees Celsius when the input F is in degrees Fahrenheit."
- This option accurately describes the function: it converts a Fahrenheit temperature to a Celsius temperature.
- Option 2: "C(F) represents the output of the function F in degrees Fahrenheit when the input C is in degrees Celsius."
- Incorrect: This suggests the reverse process, a conversion from Celsius to Fahrenheit, which the given function does not do.
- Option 3: "C(F) represents the output of the function C in degrees Fahrenheit when the input F is in degrees Celsius."
- Incorrect: This suggests that the output is in Fahrenheit, which is not what the function does.
- Option 4: "C(F) represents the output of the function F in degrees Celsius when the input C is in degrees Fahrenheit."
- Incorrect: The function [tex]\( C \)[/tex] is not taking Celsius input nor is it outputting Fahrenheit.
Based on this analysis, the correct interpretation of what [tex]\( C(F) \)[/tex] represents is:
"C(F) represents the output of the function C in degrees Celsius when the input F is in degrees Fahrenheit."
1. Identify the Function's Purpose:
- The function [tex]\( C(F) \)[/tex] is designed to convert temperatures from degrees Fahrenheit to degrees Celsius.
- In this function:
- [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit (the input).
- [tex]\( C(F) \)[/tex] is the temperature in degrees Celsius (the output).
2. Understanding the Function Notation:
- In the notation [tex]\( C(F) \)[/tex], [tex]\( C \)[/tex] indicates that it is a function that calculates Celsius temperatures.
- The variable [tex]\( F \)[/tex] inside the parenthesis represents the input of the function, which is the temperature in Fahrenheit.
3. Interpret the Output:
- When you input a Fahrenheit temperature into the function [tex]\( C(F) \)[/tex], it processes this input and provides an output in degrees Celsius.
- Therefore, [tex]\( C(F) \)[/tex] gives the temperature in degrees Celsius corresponding to the provided Fahrenheit temperature.
4. Match with Given Options:
- Option 1: "C(F) represents the output of the function C in degrees Celsius when the input F is in degrees Fahrenheit."
- This option accurately describes the function: it converts a Fahrenheit temperature to a Celsius temperature.
- Option 2: "C(F) represents the output of the function F in degrees Fahrenheit when the input C is in degrees Celsius."
- Incorrect: This suggests the reverse process, a conversion from Celsius to Fahrenheit, which the given function does not do.
- Option 3: "C(F) represents the output of the function C in degrees Fahrenheit when the input F is in degrees Celsius."
- Incorrect: This suggests that the output is in Fahrenheit, which is not what the function does.
- Option 4: "C(F) represents the output of the function F in degrees Celsius when the input C is in degrees Fahrenheit."
- Incorrect: The function [tex]\( C \)[/tex] is not taking Celsius input nor is it outputting Fahrenheit.
Based on this analysis, the correct interpretation of what [tex]\( C(F) \)[/tex] represents is:
"C(F) represents the output of the function C in degrees Celsius when the input F is in degrees Fahrenheit."