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 context of the given function, we need to understand how the function is being used to convert temperatures.

The function provided is [tex]$\subset(F) = \frac{5}{9}(F - 32)$[/tex]. This function is used to convert a temperature in degrees Fahrenheit ([tex]$F$[/tex]) to degrees Celsius. Here's a step-by-step explanation:

1. Identify the Purpose of the Function:
- The function [tex]$\subset(F) = \frac{5}{9}(F - 32)$[/tex] is a standard formula for converting temperatures from Fahrenheit to Celsius.

2. Understand the Components:
- [tex]$F$[/tex] is the input, representing a temperature in degrees Fahrenheit.
- The expression [tex]$\frac{5}{9}(F - 32)$[/tex] calculates the equivalent temperature in degrees Celsius.

3. Analyze What [tex]$C(F)$[/tex] Represents:
- The notation [tex]$C(F)$[/tex] indicates that [tex]$C$[/tex] is a function of [tex]$F$[/tex]. Therefore, [tex]$C(F)$[/tex] gives the temperature in degrees Celsius corresponding to the input temperature [tex]$F$[/tex] in degrees Fahrenheit.

Given this context, let's match it with the options provided:

- 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 option accurately describes the conversion process. Thus, [tex]$C(F)$[/tex] is the temperature in degrees Celsius that you get after converting from degrees Fahrenheit. Therefore, the correct representation of [tex]$C(F)$[/tex] is described by 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.