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 :

Certainly! Let's solve this problem step-by-step.

Siera wants to convert a temperature from degrees Fahrenheit to degrees Celsius. To do this, she's using the function [tex]\( C(F) = \frac{5}{9} (F - 32) \)[/tex].

1. Understanding the Function:
- The function [tex]\( C(F) \)[/tex] takes an input [tex]\( F \)[/tex], which represents the temperature in degrees Fahrenheit.
- It then applies the formula [tex]\( \frac{5}{9} (F - 32) \)[/tex] to convert this temperature from Fahrenheit to Celsius.

2. Breaking Down the Formula:
- The formula [tex]\( \frac{5}{9} (F - 32) \)[/tex] is a standard conversion formula from Fahrenheit to Celsius.
- The steps involved in this calculation include subtracting 32 from the Fahrenheit temperature and then multiplying the result by [tex]\(\frac{5}{9}\)[/tex].

3. What [tex]\( C(F) \)[/tex] Represents:
- The function outputs a value in degrees Celsius, which is the converted temperature from the original Fahrenheit input.
- Therefore, [tex]\( C(F) \)[/tex] gives us the temperature in Celsius for the corresponding Fahrenheit input.

4. Correct Interpretation of [tex]\( C(F) \)[/tex]:
- Based on the explanation above, [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.

So, the correct answer is:

[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.