High School

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 :

The function is given by

[tex]$$
C(F) = \frac{5}{9}(F - 32).
$$[/tex]

This equation is used to convert a temperature from degrees Fahrenheit to degrees Celsius. Here’s the step-by-step explanation:

1. The variable [tex]\( F \)[/tex] represents the temperature in degrees Fahrenheit.
2. The function [tex]\( C(F) \)[/tex] takes the temperature [tex]\( F \)[/tex] as input.
3. The expression [tex]\( F - 32 \)[/tex] adjusts the Fahrenheit temperature by subtracting 32.
4. The factor [tex]\( \frac{5}{9} \)[/tex] then scales this adjusted value to give the temperature in degrees Celsius.
5. Thus, [tex]\( C(F) \)[/tex] outputs the temperature in degrees Celsius when a temperature [tex]\( F \)[/tex] in degrees Fahrenheit is input.

Therefore, [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.