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 understand what [tex]$C(F)$[/tex] represents, let's break down the function provided:

The function given is [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex].

This is a conversion formula used to convert temperatures from degrees Fahrenheit to degrees Celsius. Here's how it works:

1. Identify the components:
- [tex]\( F \)[/tex] is the input to the function, representing temperature in degrees Fahrenheit.
- [tex]\( C(F) \)[/tex] is the output of the function, representing temperature in degrees Celsius.

2. Understand the formula:
- The formula [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] calculates the Celsius equivalent of a given Fahrenheit temperature.
- The formula works by first subtracting 32 from the Fahrenheit temperature, which adjusts for the offset between the starting points of the two temperature scales.
- Then, multiplying by [tex]\(\frac{5}{9}\)[/tex] accounts for the difference in the size of the degree units on the two scales.

3. Interpret what [tex]\( C(F) \)[/tex] represents:
- Since [tex]\( C(F) \)[/tex] is the result of applying this conversion formula, it represents the temperature in degrees Celsius that corresponds to the input temperature in degrees Fahrenheit.

Given these steps, we can conclude:

[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.