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 given is

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

This means that if you input a temperature in degrees Fahrenheit ([tex]$F$[/tex]), the function calculates the corresponding temperature in degrees Celsius. Here is the step-by-step reasoning:

1. In function notation, the notation [tex]$C(F)$[/tex] denotes that the function [tex]$C$[/tex] takes an input value [tex]$F$[/tex]. In this context, [tex]$F$[/tex] is the temperature in degrees Fahrenheit.

2. The formula

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

converts the Fahrenheit temperature to Celsius. The operations performed on [tex]$F$[/tex] (subtracting [tex]$32$[/tex], then multiplying by [tex]$\frac{5}{9}$[/tex]) follow the standard conversion formula from degrees Fahrenheit to degrees Celsius.

3. Since the output of the function is the Celsius temperature, [tex]$C(F)$[/tex] represents the value of the temperature in degrees Celsius corresponding to an input temperature [tex]$F$[/tex] given in degrees Fahrenheit.

Thus, the correct interpretation is:

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