Answer :
To solve this problem, we need to understand what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] represents. This function is used to convert a temperature from degrees Fahrenheit to degrees Celsius.
Here's a step-by-step explanation:
1. Identify the Purpose of the Function:
- The function [tex]\( C(F) \)[/tex] is designed to convert temperatures. The formula specifies that when you input a temperature in degrees Fahrenheit, it performs a specific calculation to give you the corresponding temperature in degrees Celsius.
2. Understand the Components of the Function:
- In the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex]:
- [tex]\( F \)[/tex] represents the input temperature in degrees Fahrenheit.
- The expression [tex]\( \frac{5}{9}(F - 32) \)[/tex] is the formula that converts Fahrenheit to Celsius.
3. Determine What [tex]\( C(F) \)[/tex] Means:
- The output of this function, [tex]\( C(F) \)[/tex], is the result of the conversion which is measured in degrees Celsius.
- Therefore, [tex]\( C(F) \)[/tex] gives you the temperature in Celsius when you have initially provided the temperature in Fahrenheit.
4. Select the Correct Description:
- From the options provided:
- “[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” is the correct description.
By following these steps, we understand that [tex]\( C(F) \)[/tex] indeed represents the temperature in degrees Celsius that corresponds to an input temperature in degrees Fahrenheit.
Here's a step-by-step explanation:
1. Identify the Purpose of the Function:
- The function [tex]\( C(F) \)[/tex] is designed to convert temperatures. The formula specifies that when you input a temperature in degrees Fahrenheit, it performs a specific calculation to give you the corresponding temperature in degrees Celsius.
2. Understand the Components of the Function:
- In the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex]:
- [tex]\( F \)[/tex] represents the input temperature in degrees Fahrenheit.
- The expression [tex]\( \frac{5}{9}(F - 32) \)[/tex] is the formula that converts Fahrenheit to Celsius.
3. Determine What [tex]\( C(F) \)[/tex] Means:
- The output of this function, [tex]\( C(F) \)[/tex], is the result of the conversion which is measured in degrees Celsius.
- Therefore, [tex]\( C(F) \)[/tex] gives you the temperature in Celsius when you have initially provided the temperature in Fahrenheit.
4. Select the Correct Description:
- From the options provided:
- “[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” is the correct description.
By following these steps, we understand that [tex]\( C(F) \)[/tex] indeed represents the temperature in degrees Celsius that corresponds to an input temperature in degrees Fahrenheit.