College

For one month, Siera calculated her hometown's average high temperature in degrees Fahrenheit. She wants to convert that temperature from degrees Fahrenheit to degrees Celsius using the function [tex]$C(F) = \frac{5}{9}(F-32)$[/tex]. What does [tex]$C(F)$[/tex] represent?

A. [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.

B. [tex]$C(F)$[/tex] represents the output of the function [tex]$F$[/tex] in degrees Fahrenheit when the input [tex]$C$[/tex] is in degrees Celsius.

C. [tex]$C(F)$[/tex] represents the output of the function [tex]$C$[/tex] in degrees Fahrenheit when the input [tex]$F$[/tex] is in degrees Celsius.

D. [tex]$C(F)$[/tex] represents the output of the function [tex]$F$[/tex] in degrees Celsius when the input [tex]$C$[/tex] is in degrees Fahrenheit.

Answer :

To understand what [tex]\( C(F) \)[/tex] represents in the function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex], let's break it down:

1. Identify the Variables:
- [tex]\( F \)[/tex] represents a temperature in degrees Fahrenheit. This is the input of the function.

2. Understand the Function:
- The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is used to convert a temperature from degrees Fahrenheit to degrees Celsius. This is a standard formula for temperature conversion.

3. Apply the Mathematical Operation:
- Subtract 32 from the Fahrenheit temperature ([tex]\( F \)[/tex]). This adjusts the input correctly as 32°F is the freezing point of water and is used as a baseline in the conversion.
- Multiply the result by [tex]\( \frac{5}{9} \)[/tex]. This scales down the adjusted temperature from Fahrenheit to Celsius, as there are 5 Celsius degrees for every 9 Fahrenheit degrees.

4. Interpret the Output:
- The result of the function, [tex]\( C(F) \)[/tex], will give the corresponding temperature in degrees Celsius.

5. Conclusion:
- Therefore, [tex]\( C(F) \)[/tex] represents the output of the function in degrees Celsius when the input [tex]\( F \)[/tex] is in degrees Fahrenheit.

This means the correct interpretation 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.