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 determine what [tex]$C(F)$[/tex] represents in the given function, let's analyze the components of the function and its purpose.

The function provided is:

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

This mathematical formula is commonly used to convert temperatures from degrees Fahrenheit to degrees Celsius. To understand what [tex]$C(F)$[/tex] represents, let's break it down:

1. Identify the Variables and Parameters:
- The function is denoted as [tex]$C(F)$[/tex], where [tex]$C$[/tex] stands for Celsius and [tex]$F$[/tex] stands for Fahrenheit.
- The input, [tex]$F$[/tex], is the temperature in degrees Fahrenheit.

2. Understand the Formula:
- The operation [tex]$(F - 32)$[/tex] adjusts the Fahrenheit temperature by subtracting 32, which aligns with the freezing point of water in the Fahrenheit scale (32°F = 0°C).
- Multiplying the result by [tex]$\frac{5}{9}$[/tex] converts the adjusted temperature from the Fahrenheit scale to the Celsius scale.

3. Determine the Output:
- The function outputs a temperature in degrees Celsius, which is denoted as [tex]$C(F)$[/tex]. This means for any input [tex]$F$[/tex], the function calculates the corresponding temperature in degrees Celsius.

Given this analysis, the correct interpretation of [tex]$C(F)$[/tex] is that it represents the output of the function [tex]$C$[/tex] in degrees Celsius when the input [tex]$F$[/tex] is in degrees Fahrenheit.

Therefore, the correct choice 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.