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 :

We are given the conversion function

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

which converts a temperature from degrees Fahrenheit to degrees Celsius.

Here is a step-by-step explanation:

1. The function takes an input [tex]$F$[/tex], which is the temperature in degrees Fahrenheit.

2. In the function, the term [tex]$(F - 32)$[/tex] subtracts 32 from the Fahrenheit temperature, accounting for the difference between the starting points of the Fahrenheit and Celsius scales.

3. Multiplying by [tex]$\frac{5}{9}$[/tex] scales the difference [tex]$F - 32$[/tex] so that it is correctly converted into degrees Celsius.

4. Thus, the output [tex]$C(F)$[/tex] is the temperature expressed in degrees Celsius.

Therefore, [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.

The correct choice is:

1. [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.