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 :

The conversion function is given by

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

where [tex]$F$[/tex] is the temperature in degrees Fahrenheit. This function subtracts [tex]$32$[/tex] from the Fahrenheit temperature (to account for the difference in the zero points of the two scales) and then multiplies the result by [tex]$\frac{5}{9}$[/tex] to convert the difference to degrees Celsius.

Thus, for any temperature [tex]$F$[/tex] (in degrees Fahrenheit), [tex]$C(F)$[/tex] is the corresponding temperature in degrees Celsius. In other words,

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

Therefore, the correct answer is the option stating that [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.