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]\[ C(F) = -\frac{5}{9} \][/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, we need to understand the purpose of the function [tex]$C(F)$[/tex]. The problem describes a situation where Siera wants to convert temperatures from degrees Fahrenheit to degrees Celsius.

Let's consider the formula for converting Fahrenheit to Celsius:

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

In this formula:

- [tex]\( C \)[/tex] is the temperature in degrees Celsius.
- [tex]\( F \)[/tex] is the temperature in degrees Fahrenheit.
- The conversion involves subtracting 32 from the Fahrenheit temperature, then multiplying by [tex]\(\frac{5}{9}\)[/tex].

Given this context, let's analyze the options provided:

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 statement correctly describes the function. Here, the function [tex]$C(F)$[/tex] outputs a temperature in degrees Celsius after converting the input temperature from degrees Fahrenheit.

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 statement is incorrect. The function is meant to output Celsius, not Fahrenheit, and the input is in Fahrenheit, not Celsius.

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 statement is incorrect. It reverses the roles of Celsius and Fahrenheit in the function's interpretation.

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 statement is incorrect because it suggests that [tex]$F$[/tex] is a function, which it is not in this context.

After analyzing these options, the correct interpretation of [tex]$C(F)$[/tex] is the first option:

- [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.

Hence, the correct option is the first one.