Answer :
To understand what [tex]\( C(F) \)[/tex] represents, let's break down the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex]. This function is used to convert a temperature from degrees Fahrenheit ([tex]\( F \)[/tex]) to degrees Celsius ([tex]\( C(F) \)[/tex]).
Here's how the function works:
1. Start with the Fahrenheit Temperature ([tex]\( F \)[/tex]): This is the temperature you begin with, measured in degrees Fahrenheit.
2. Subtract 32 from the Fahrenheit Temperature: The number 32 is subtracted because it's the offset for the freezing point of water in the Fahrenheit scale, which is 32°F. The formula for conversion first normalizes the temperature by taking into account this offset.
3. Multiply by [tex]\(\frac{5}{9}\)[/tex]: This fraction adjusts for the different sizes of the units on the Celsius and Fahrenheit scales. The Celsius scale has 100 units between the freezing and boiling points of water, while the Fahrenheit scale has 180 units between the same points. Therefore, the conversion factor is [tex]\(\frac{5}{9}\)[/tex].
4. Output the Temperature in Degrees Celsius ([tex]\( C(F) \)[/tex]): After these calculations, the result is the equivalent temperature on the Celsius scale.
Given all this information, the statement that best describes what [tex]\( C(F) \)[/tex] represents 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 that if you input a certain temperature in Fahrenheit into the function, it will provide the corresponding temperature in Celsius.
Here's how the function works:
1. Start with the Fahrenheit Temperature ([tex]\( F \)[/tex]): This is the temperature you begin with, measured in degrees Fahrenheit.
2. Subtract 32 from the Fahrenheit Temperature: The number 32 is subtracted because it's the offset for the freezing point of water in the Fahrenheit scale, which is 32°F. The formula for conversion first normalizes the temperature by taking into account this offset.
3. Multiply by [tex]\(\frac{5}{9}\)[/tex]: This fraction adjusts for the different sizes of the units on the Celsius and Fahrenheit scales. The Celsius scale has 100 units between the freezing and boiling points of water, while the Fahrenheit scale has 180 units between the same points. Therefore, the conversion factor is [tex]\(\frac{5}{9}\)[/tex].
4. Output the Temperature in Degrees Celsius ([tex]\( C(F) \)[/tex]): After these calculations, the result is the equivalent temperature on the Celsius scale.
Given all this information, the statement that best describes what [tex]\( C(F) \)[/tex] represents 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 that if you input a certain temperature in Fahrenheit into the function, it will provide the corresponding temperature in Celsius.