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 go through the options to determine what [tex]$C(F)$[/tex] represents:

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

This function is used to convert temperatures from degrees Fahrenheit ([tex]\(F\)[/tex]) to degrees Celsius ([tex]\(C\)[/tex]).

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.

- Here, we input a temperature in degrees Fahrenheit ([tex]\(F\)[/tex]) into the function [tex]\(C(F) = \frac{5}{9}(F - 32)\)[/tex].
- The output, [tex]\(C(F)\)[/tex], gives us the temperature in degrees Celsius.
- This matches the purpose of the conversion formula, which is to convert from Fahrenheit to Celsius.

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 suggests that [tex]\(C(F)\)[/tex] would give a Fahrenheit output, which is incorrect since the formula is for converting to 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 implies that [tex]\(C(F)\)[/tex] outputs Fahrenheit temperatures from a Celsius input, which doesn't match the conversion function we were given.

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 also incorrectly describes the function; it suggests getting Celsius output from Fahrenheit input, but mentions a function [tex]$F$[/tex], which is not correct here.

Given these options, the first one accurately describes the function: [tex]\( C(F) = \frac{5}{9}(F - 32) \)[/tex] represents the conversion of a temperature from Fahrenheit to Celsius. 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.