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 converts a temperature [tex]$F$[/tex] in degrees Fahrenheit to its equivalent in degrees Celsius.

Step 1: Identify the input and output.
The variable [tex]$F$[/tex] in the expression is the temperature in degrees Fahrenheit, and the function [tex]$C(F)$[/tex] computes the corresponding temperature in degrees Celsius.

Step 2: Interpret the function.
Since the formula subtracts 32 from [tex]$F$[/tex], multiplies by [tex]$5$[/tex], and then divides by [tex]$9$[/tex], it clearly converts the Fahrenheit measurement to Celsius.

Step 3: Write the meaning in words.
Thus, [tex]$C(F)$[/tex] represents the output of the function [tex]$C$[/tex], which is the temperature in degrees Celsius when a Fahrenheit temperature [tex]$F$[/tex] is provided as input.

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