Answer :
To understand what [tex]\( C(F) \)[/tex] represents, let's break down the given function and options:
1. The Function:
- The function given is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
- This is the formula used to convert a temperature in degrees Fahrenheit ([tex]\( F \)[/tex]) to degrees Celsius ([tex]\( C \)[/tex]).
2. Understanding the Function:
- The input to the function is [tex]\( F \)[/tex], which stands for the temperature in degrees Fahrenheit.
- The function calculates the corresponding temperature in degrees Celsius, which is the output and denoted by [tex]\( C(F) \)[/tex].
3. Identifying the Correct Interpretation:
- The key point is recognizing that the input ([tex]\( F \)[/tex]) is in Fahrenheit and the output ([tex]\( C(F) \)[/tex]) is in Celsius.
4. Option Analysis:
- Option 1: [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 option is correct because it accurately describes the conversion of Fahrenheit to Celsius using the function.
- Option 2: [tex]\( C(F) \)[/tex] 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, as [tex]\( C(F) \)[/tex] actually converts from Fahrenheit to Celsius.
- Option 3: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Fahrenheit when the input [tex]\( F \)[/tex] is in degrees Celsius.
- This is incorrect, as the function converts to Celsius, not Fahrenheit.
- Option 4: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( F \)[/tex] in degrees Celsius when the input [tex]\( C \)[/tex] is in degrees Fahrenheit.
- This is incorrect because it confuses the roles of [tex]\( C \)[/tex] and [tex]\( F \)[/tex].
Thus, the correct interpretation is that [tex]\( C(F) \)[/tex] represents the output temperature in degrees Celsius when the input temperature is in degrees Fahrenheit. Therefore, Option 1 is the correct choice.
1. The Function:
- The function given is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
- This is the formula used to convert a temperature in degrees Fahrenheit ([tex]\( F \)[/tex]) to degrees Celsius ([tex]\( C \)[/tex]).
2. Understanding the Function:
- The input to the function is [tex]\( F \)[/tex], which stands for the temperature in degrees Fahrenheit.
- The function calculates the corresponding temperature in degrees Celsius, which is the output and denoted by [tex]\( C(F) \)[/tex].
3. Identifying the Correct Interpretation:
- The key point is recognizing that the input ([tex]\( F \)[/tex]) is in Fahrenheit and the output ([tex]\( C(F) \)[/tex]) is in Celsius.
4. Option Analysis:
- Option 1: [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 option is correct because it accurately describes the conversion of Fahrenheit to Celsius using the function.
- Option 2: [tex]\( C(F) \)[/tex] 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, as [tex]\( C(F) \)[/tex] actually converts from Fahrenheit to Celsius.
- Option 3: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( C \)[/tex] in degrees Fahrenheit when the input [tex]\( F \)[/tex] is in degrees Celsius.
- This is incorrect, as the function converts to Celsius, not Fahrenheit.
- Option 4: [tex]\( C(F) \)[/tex] represents the output of the function [tex]\( F \)[/tex] in degrees Celsius when the input [tex]\( C \)[/tex] is in degrees Fahrenheit.
- This is incorrect because it confuses the roles of [tex]\( C \)[/tex] and [tex]\( F \)[/tex].
Thus, the correct interpretation is that [tex]\( C(F) \)[/tex] represents the output temperature in degrees Celsius when the input temperature is in degrees Fahrenheit. Therefore, Option 1 is the correct choice.