Answer :
To solve the question about what [tex]$C(F)$[/tex] represents when converting temperatures from degrees Fahrenheit to degrees Celsius using the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex], let's break down what each part of the function and its terms mean.
1. Function Definition:
- The function is defined as [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
- Here, [tex]\( C(F) \)[/tex] represents the output of the function, which gives us a temperature value.
- The input to the function is [tex]\( F \)[/tex], which represents the temperature in degrees Fahrenheit.
2. Purpose of the Function:
- The function's purpose is to convert a temperature from degrees Fahrenheit to degrees Celsius. This is evident from the formula:
- The term [tex]\( (F - 32) \)[/tex] adjusts for the difference in the starting point of the Fahrenheit and Celsius scales.
- Multiplying by [tex]\(\frac{5}{9}\)[/tex] converts the interval size (how temperature scales measure changes in temperature) from Fahrenheit to Celsius.
3. Interpreting [tex]$C(F)$[/tex]:
- The notation [tex]\( C(F) \)[/tex] means we are taking a Fahrenheit temperature, processing it through the function, and obtaining a Celsius temperature.
- Therefore, [tex]\( C(F) \)[/tex] is indeed a Celsius temperature after conversion from the Fahrenheit input.
4. Choosing the Correct Option:
- Based on the explanation above, the correct interpretation is that [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.
Therefore, the correct option is: "[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."
1. Function Definition:
- The function is defined as [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].
- Here, [tex]\( C(F) \)[/tex] represents the output of the function, which gives us a temperature value.
- The input to the function is [tex]\( F \)[/tex], which represents the temperature in degrees Fahrenheit.
2. Purpose of the Function:
- The function's purpose is to convert a temperature from degrees Fahrenheit to degrees Celsius. This is evident from the formula:
- The term [tex]\( (F - 32) \)[/tex] adjusts for the difference in the starting point of the Fahrenheit and Celsius scales.
- Multiplying by [tex]\(\frac{5}{9}\)[/tex] converts the interval size (how temperature scales measure changes in temperature) from Fahrenheit to Celsius.
3. Interpreting [tex]$C(F)$[/tex]:
- The notation [tex]\( C(F) \)[/tex] means we are taking a Fahrenheit temperature, processing it through the function, and obtaining a Celsius temperature.
- Therefore, [tex]\( C(F) \)[/tex] is indeed a Celsius temperature after conversion from the Fahrenheit input.
4. Choosing the Correct Option:
- Based on the explanation above, the correct interpretation is that [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.
Therefore, the correct option is: "[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."