Answer :
To solve the given problem, we need to understand what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] represents:
1. Identify the Purpose of the Function:
- The function [tex]\( C(F) \)[/tex] is used to convert a temperature value from degrees Fahrenheit (indicated by [tex]\( F \)[/tex]) to degrees Celsius.
2. Understanding the Notation:
- [tex]\( C(F) \)[/tex] indicates that the function uses [tex]\( F \)[/tex] (a temperature given in Fahrenheit) as an input and produces an output.
- The formula involves subtracting 32 from the Fahrenheit temperature and then multiplying the result by [tex]\(\frac{5}{9}\)[/tex], which is the standard formula to convert Fahrenheit to Celsius.
3. Analyze the Answer Choices:
- Choice 1: "C(F) represents the output of the function C in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit."
- This describes exactly what the function does: it converts temperatures from Fahrenheit to Celsius.
- Choice 2: "C(F) represents the output of the function [tex]\( F \)[/tex] in degrees Fahrenheit when the input [tex]\( C \)[/tex] is in degrees Celsius."
- This is incorrect because it reverses the roles of the variables and the conversion direction.
- Choice 3: "C(F) represents the output of the function [tex]\( C \)[/tex] in degrees Fahrenheit when the input [tex]\( F \)[/tex] is in degrees Gelsius."
- This contains a typo and also suggests the wrong temperature conversion direction.
- Choice 4: "C(F) represents the output of the function [tex]\( F \)[/tex] in degrees Celsius when the input [tex]\( C \)[/tex] is in degrees Fahrenheit."
- This option confuses the roles of the inputs and outputs; it does not describe the conversion correctly.
4. Conclusion:
- Based on the definitions and purpose of the function, the correct choice is the first one: "C(F) represents the output of the function C in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit."
This is the correct interpretation of what [tex]\( C(F) \)[/tex] represents, as it aligns with the function’s role in converting a Fahrenheit temperature to Celsius.
1. Identify the Purpose of the Function:
- The function [tex]\( C(F) \)[/tex] is used to convert a temperature value from degrees Fahrenheit (indicated by [tex]\( F \)[/tex]) to degrees Celsius.
2. Understanding the Notation:
- [tex]\( C(F) \)[/tex] indicates that the function uses [tex]\( F \)[/tex] (a temperature given in Fahrenheit) as an input and produces an output.
- The formula involves subtracting 32 from the Fahrenheit temperature and then multiplying the result by [tex]\(\frac{5}{9}\)[/tex], which is the standard formula to convert Fahrenheit to Celsius.
3. Analyze the Answer Choices:
- Choice 1: "C(F) represents the output of the function C in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit."
- This describes exactly what the function does: it converts temperatures from Fahrenheit to Celsius.
- Choice 2: "C(F) represents the output of the function [tex]\( F \)[/tex] in degrees Fahrenheit when the input [tex]\( C \)[/tex] is in degrees Celsius."
- This is incorrect because it reverses the roles of the variables and the conversion direction.
- Choice 3: "C(F) represents the output of the function [tex]\( C \)[/tex] in degrees Fahrenheit when the input [tex]\( F \)[/tex] is in degrees Gelsius."
- This contains a typo and also suggests the wrong temperature conversion direction.
- Choice 4: "C(F) represents the output of the function [tex]\( F \)[/tex] in degrees Celsius when the input [tex]\( C \)[/tex] is in degrees Fahrenheit."
- This option confuses the roles of the inputs and outputs; it does not describe the conversion correctly.
4. Conclusion:
- Based on the definitions and purpose of the function, the correct choice is the first one: "C(F) represents the output of the function C in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit."
This is the correct interpretation of what [tex]\( C(F) \)[/tex] represents, as it aligns with the function’s role in converting a Fahrenheit temperature to Celsius.