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 :

Sure! Let's break down the problem step by step to understand what [tex]\( C(F) \)[/tex] represents in the context of temperature conversion.

You are provided with the function:
[tex]\[ C(F) = \frac{5}{9}(F - 32) \][/tex]

This function is used for converting temperatures from degrees Fahrenheit to degrees Celsius. Let's analyze the options:

1. Option 1: [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.
- This is a correct interpretation. The function [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] takes a temperature in Fahrenheit (denoted by [tex]\( F \)[/tex]) and converts it to Celsius (denoted by [tex]\( C \)[/tex]).

2. Option 2: [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.
- This is not correct because [tex]\( C(F) \)[/tex] is not a function to calculate Fahrenheit. Instead, it converts a Fahrenheit input into Celsius.

3. Option 3: [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.
- This option is incorrect because the function actually provides a temperature output in Celsius, not Fahrenheit.

4. Option 4: [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.
- This is incorrect because it reverses the role of input and output. [tex]\( F \)[/tex] is the input in Fahrenheit, and [tex]\( C \)[/tex] is the output in Celsius.

After reviewing all options, we can determine that Option 1 is the best choice. It accurately describes the conversion process that the function performs:
[tex]\[ C(F) \][/tex] converts the input temperature in degrees Fahrenheit to an output temperature in degrees Celsius.