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 conversion function is given by

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

Here’s a step-by-step explanation:

1. The variable [tex]$F$[/tex] represents a temperature in degrees Fahrenheit.
2. The function subtracts 32 from [tex]$F$[/tex], which adjusts the scale by accounting for the freezing point of water in Fahrenheit.
3. The product [tex]$\frac{5}{9}$[/tex] scales the difference so that it is in degrees Celsius.
4. Therefore, when you input a temperature in Fahrenheit into this function, the output [tex]$C(F)$[/tex] is the equivalent temperature in degrees Celsius.

Thus, [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.