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 are given the conversion function:

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

which means that for any temperature given in degrees Fahrenheit (represented by [tex]$F$[/tex]), the function computes the corresponding temperature in degrees Celsius.

Step-by-step explanation:

1. The function [tex]$C(F)$[/tex] takes an input [tex]$F$[/tex], which is the temperature in degrees Fahrenheit.
2. It subtracts 32 from [tex]$F$[/tex] and then multiplies the result by [tex]$\frac{5}{9}$[/tex].
3. The resulting value is the temperature expressed in degrees Celsius.
4. Therefore, [tex]$C(F)$[/tex] represents the temperature in degrees Celsius when [tex]$F$[/tex] is the temperature in degrees Fahrenheit.

Thus, the correct interpretation is:

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