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 :

To solve this question, we need to understand what [tex]$C(F)$[/tex] represents in the context of the function given. The function provided is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].

Let's break this down:

1. Input and Output of the Function:
- The function [tex]\( C(F) \)[/tex] is designed to take an input in degrees Fahrenheit (denoted by [tex]\( F \)[/tex]) and convert it to degrees Celsius (denoted by [tex]\( C \)[/tex]).

2. Understanding the Formula:
- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] is a standard formula used to convert temperatures from Fahrenheit to Celsius.
- Here's how it works:
- Subtract 32 from the Fahrenheit temperature (this adjusts for the starting point difference between the two scales).
- Multiply the result by [tex]\(\frac{5}{9}\)[/tex] to scale the difference from Fahrenheit's larger degree interval to Celsius's smaller degree interval.

3. Interpreting [tex]\( C(F) \)[/tex]:
- [tex]\( C(F) \)[/tex] is the notation for the output of this conversion function. It gives the result in degrees Celsius for a given temperature in degrees Fahrenheit.

So, in simple terms, [tex]\( C(F) \)[/tex] represents the temperature in degrees Celsius that corresponds to an input temperature [tex]\( F \)[/tex] in degrees Fahrenheit.

Therefore, the correct interpretation 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.