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 :

To solve the question about what [tex]$C(F)$[/tex] represents, start by looking at the function given:

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

This formula is used to convert a temperature from degrees Fahrenheit (F) to degrees Celsius (C).

Here's a breakdown of the function:

1. Input: The function's input is the temperature in degrees Fahrenheit, represented by [tex]\( F \)[/tex].
2. Operation: The function performs a conversion operation on this input by subtracting 32 from the Fahrenheit temperature and then multiplying by [tex]\(\frac{5}{9}\)[/tex].
3. Output: The result of these operations is the temperature in degrees Celsius, which is what [tex]\( C(F) \)[/tex] represents.

Therefore, [tex]\( C(F) \)[/tex] represents the temperature after it's been converted from Fahrenheit to Celsius. The function effectively tells us the equivalent temperature in Celsius based on the Fahrenheit temperature provided.

Hence, the correct interpretation of [tex]\( C(F) \)[/tex] 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.