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 :

We have the conversion function
$$
C(F) = \frac{5}{9}(F-32),
$$
which takes as input a temperature in degrees Fahrenheit (denoted by $F$) and outputs the corresponding temperature in degrees Celsius.

Step-by-step explanation:

1. The input variable $F$ represents a temperature in degrees Fahrenheit.
2. The function subtracts 32 from $F$, which is a necessary adjustment when converting Fahrenheit to Celsius.
3. Multiplying by $\frac{5}{9}$ scales the result to give the temperature in Celsius.
4. Thus, the expression $C(F)$ yields the temperature in degrees Celsius corresponding to the Fahrenheit temperature $F$.

Therefore, $C(F)$ represents the output of the function $C$ in degrees Celsius when the input $F$ is in degrees Fahrenheit.