To determine what the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] represents, let's break down the components of the function and what each part means.
1. Variable [tex]\( F \)[/tex]: This represents the temperature measured in degrees Fahrenheit.
2. Expression [tex]\( F - 32 \)[/tex]: In this part of the function, we take the temperature in degrees Fahrenheit and subtract 32 from it. This is necessary because 32 degrees Fahrenheit is the freezing point of water, which is 0 degrees in Celsius. This subtraction aligns the Fahrenheit scale with the Celsius scale at the freezing point of water.
3. Factor [tex]\( \frac{5}{9} \)[/tex]: This fraction is used to convert the difference in temperature from Fahrenheit to Celsius. It's derived from the ratio of the size of one degree Fahrenheit to the size of one degree Celsius. Specifically, the temperature change of 1 degree Fahrenheit is equivalent to [tex]\( \frac{5}{9} \)[/tex] of a degree Celsius.
4. Combining these parts: The whole function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] converts a temperature from degrees Fahrenheit to degrees Celsius.
Therefore, the function [tex]\( C(F) \)[/tex] signifies the temperature in degrees Fahrenheit, denoted by [tex]\( F \)[/tex], being converted to degrees Celsius.
Given this explanation, the correct choice among the available options is:
the temperature of [tex]\( F \)[/tex] degrees Fahrenheit converted to degrees Celsius
