Answer :
Certainly! Let's break down the problem to understand what [tex]$C(F)$[/tex] represents.
1. Understanding the Function [tex]$C(F)$[/tex]:
The function given is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex]. This mathematical function is used to convert a temperature from degrees Fahrenheit to degrees Celsius.
2. Identifying the Variables:
- [tex]\( F \)[/tex]: The input of the function, which represents the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex]: The output, which represents the converted temperature in degrees Celsius.
3. Purpose of the Function:
The function takes a temperature in Fahrenheit ([tex]\( F \)[/tex]) and converts it into Celsius ([tex]\( C \)[/tex]) using the formula:
[tex]\[
C = \frac{5}{9} \times (F - 32)
\][/tex]
This formula originates from the relationship between the Fahrenheit and Celsius temperature scales.
4. Analyzing the Options:
- Option 1: "C(F) represents the output of the function C in degrees Celsius when the input F is in degrees Fahrenheit."
This correctly describes the function since it states that the function outputs a temperature in degrees Celsius given a temperature in degrees Fahrenheit.
- The other options do not accurately describe the relationship that the function [tex]\( C(F) \)[/tex] represents. They either mix up the units or describe the conversion in the wrong direction.
5. Conclusion:
Based on the analysis, [tex]$C(F)$[/tex] indeed represents the output of the function in degrees Celsius when the input is in degrees Fahrenheit.
Therefore, the correct answer 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. Understanding the Function [tex]$C(F)$[/tex]:
The function given is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex]. This mathematical function is used to convert a temperature from degrees Fahrenheit to degrees Celsius.
2. Identifying the Variables:
- [tex]\( F \)[/tex]: The input of the function, which represents the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex]: The output, which represents the converted temperature in degrees Celsius.
3. Purpose of the Function:
The function takes a temperature in Fahrenheit ([tex]\( F \)[/tex]) and converts it into Celsius ([tex]\( C \)[/tex]) using the formula:
[tex]\[
C = \frac{5}{9} \times (F - 32)
\][/tex]
This formula originates from the relationship between the Fahrenheit and Celsius temperature scales.
4. Analyzing the Options:
- Option 1: "C(F) represents the output of the function C in degrees Celsius when the input F is in degrees Fahrenheit."
This correctly describes the function since it states that the function outputs a temperature in degrees Celsius given a temperature in degrees Fahrenheit.
- The other options do not accurately describe the relationship that the function [tex]\( C(F) \)[/tex] represents. They either mix up the units or describe the conversion in the wrong direction.
5. Conclusion:
Based on the analysis, [tex]$C(F)$[/tex] indeed represents the output of the function in degrees Celsius when the input is in degrees Fahrenheit.
Therefore, the correct answer 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.