Answer :
Let's break down what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] represents:
1. Understanding the Function:
- [tex]\( C(F) \)[/tex] is a mathematical function used to convert temperatures from degrees Fahrenheit (F) to degrees Celsius (C).
- The formula [tex]\(\frac{5}{9}(F - 32)\)[/tex] is the standard conversion method between these two temperature scales.
2. Components of the Function:
- [tex]\( F \)[/tex] is the input variable, representing a temperature in degrees Fahrenheit.
- [tex]\(\frac{5}{9}\)[/tex] is the conversion factor that adjusts the scale from Fahrenheit to Celsius.
- [tex]\( (F - 32) \)[/tex] accounts for the difference in the starting point of the two temperature scales (32°F is the freezing point of water in Fahrenheit, which corresponds to 0°C in Celsius).
3. Interpreting [tex]\( C(F) \)[/tex]:
- [tex]\( C(F) \)[/tex] represents the output of the function, which is the temperature in degrees Celsius after conversion.
- By applying the formula, you input a temperature in Fahrenheit, and the function gives you the equivalent temperature in Celsius.
Among the given options, the correct interpretation that matches this understanding 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 statement accurately describes the purpose and result of using the function [tex]\( C(F) \)[/tex].
1. Understanding the Function:
- [tex]\( C(F) \)[/tex] is a mathematical function used to convert temperatures from degrees Fahrenheit (F) to degrees Celsius (C).
- The formula [tex]\(\frac{5}{9}(F - 32)\)[/tex] is the standard conversion method between these two temperature scales.
2. Components of the Function:
- [tex]\( F \)[/tex] is the input variable, representing a temperature in degrees Fahrenheit.
- [tex]\(\frac{5}{9}\)[/tex] is the conversion factor that adjusts the scale from Fahrenheit to Celsius.
- [tex]\( (F - 32) \)[/tex] accounts for the difference in the starting point of the two temperature scales (32°F is the freezing point of water in Fahrenheit, which corresponds to 0°C in Celsius).
3. Interpreting [tex]\( C(F) \)[/tex]:
- [tex]\( C(F) \)[/tex] represents the output of the function, which is the temperature in degrees Celsius after conversion.
- By applying the formula, you input a temperature in Fahrenheit, and the function gives you the equivalent temperature in Celsius.
Among the given options, the correct interpretation that matches this understanding 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 statement accurately describes the purpose and result of using the function [tex]\( C(F) \)[/tex].