To determine what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] represents, let’s carefully analyze the components of the function and what it aims to achieve.
1. Understanding the Variables:
- [tex]\( F \)[/tex]: This is the input to the function, representing the temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex]: This is the output of the function, which represents the temperature in degrees Celsius.
2. Analyzing the Formula:
- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is used to convert temperatures from Fahrenheit to Celsius.
- To convert a temperature given in Fahrenheit ([tex]\( F \)[/tex]) to Celsius ([tex]\( C \)[/tex]), we subtract 32 from the Fahrenheit value and then multiply by [tex]\(\frac{5}{9}\)[/tex].
3. Interpretation of Conversion:
- The function [tex]\( C(F) \)[/tex] takes the Fahrenheit temperature [tex]\( F \)[/tex] and converts it into its equivalent Celsius temperature [tex]\( C \)[/tex].
- Therefore, the description must state that [tex]\( C(F) \)[/tex] provides the temperature, originally in Fahrenheit, now expressed in Celsius.
4. Choosing the Correct Answer:
- The first choice, “the temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius,” correctly describes that the function converts Fahrenheit to Celsius.
- The other choices describe incorrect conversions or misuse of variables and measurements.
Hence, [tex]\( C(F) \)[/tex] represents "the temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius".
Therefore, the correct answer is: "the temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius."
This corresponds to the multiple choice answer index 1.
