Answer :
To solve this question, we need to understand what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] represents. This function is used to convert temperatures from degrees Fahrenheit to degrees Celsius.
Here's a step-by-step explanation:
1. Understand the Components:
- The input of the function is [tex]\( F \)[/tex], which represents a temperature in degrees Fahrenheit.
- The output of the function is [tex]\( C(F) \)[/tex], which gives us the equivalent temperature in degrees Celsius after applying the conversion.
2. Explain the Conversion Formula:
- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is derived from the relationship between Fahrenheit and Celsius scales.
- The formula subtracts 32 from the Fahrenheit temperature because the freezing point of water is 32°F, which corresponds to 0°C.
- It then multiplies the result by [tex]\( \frac{5}{9} \)[/tex] to adjust for the difference in scale sizes between Fahrenheit and Celsius (Fahrenheit has 180 degrees between the freezing and boiling points of water, while Celsius has 100).
3. Interpret the Function:
- [tex]\( C(F) \)[/tex] specifically represents the temperature in degrees Celsius that corresponds to an input temperature [tex]\( F \)[/tex] in degrees Fahrenheit.
4. Choose the Correct Representation:
- From the options provided:
- The first option states: "[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".
- The second option mistakenly refers to [tex]$C(F)$[/tex] as the output of the function [tex]$F$[/tex]. This does not properly describe the function given.
5. Conclusion:
- The correct interpretation of the function is that [tex]$C(F)$[/tex] represents the output 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." This means the function transforms a Fahrenheit temperature into its equivalent Celsius temperature.
Here's a step-by-step explanation:
1. Understand the Components:
- The input of the function is [tex]\( F \)[/tex], which represents a temperature in degrees Fahrenheit.
- The output of the function is [tex]\( C(F) \)[/tex], which gives us the equivalent temperature in degrees Celsius after applying the conversion.
2. Explain the Conversion Formula:
- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is derived from the relationship between Fahrenheit and Celsius scales.
- The formula subtracts 32 from the Fahrenheit temperature because the freezing point of water is 32°F, which corresponds to 0°C.
- It then multiplies the result by [tex]\( \frac{5}{9} \)[/tex] to adjust for the difference in scale sizes between Fahrenheit and Celsius (Fahrenheit has 180 degrees between the freezing and boiling points of water, while Celsius has 100).
3. Interpret the Function:
- [tex]\( C(F) \)[/tex] specifically represents the temperature in degrees Celsius that corresponds to an input temperature [tex]\( F \)[/tex] in degrees Fahrenheit.
4. Choose the Correct Representation:
- From the options provided:
- The first option states: "[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".
- The second option mistakenly refers to [tex]$C(F)$[/tex] as the output of the function [tex]$F$[/tex]. This does not properly describe the function given.
5. Conclusion:
- The correct interpretation of the function is that [tex]$C(F)$[/tex] represents the output 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." This means the function transforms a Fahrenheit temperature into its equivalent Celsius temperature.