High School

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 :

We are given the function

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

which is used to convert a temperature measured in degrees Fahrenheit ([tex]$F$[/tex]) into a temperature in degrees Celsius. Here’s the step-by-step reasoning:

1. The function takes a temperature [tex]$F$[/tex] in degrees Fahrenheit as input.

2. Inside the function, [tex]$32$[/tex] is subtracted from [tex]$F$[/tex], which accounts for the difference in the Fahrenheit and Celsius scales.

3. The result is then multiplied by [tex]$\frac{5}{9}$[/tex] (approximately [tex]$0.5556$[/tex]) to complete the conversion from Fahrenheit to Celsius.

4. Therefore, [tex]$C(F)$[/tex] is the temperature in degrees Celsius that corresponds to a temperature of [tex]$F$[/tex] degrees Fahrenheit.

Thus, the correct interpretation is:

[tex]$$
\text{"}C(F) \text{ represents the output of the function } C \text{ in degrees Celsius when the input } F \text{ is in degrees Fahrenheit."\text{ }}
$$[/tex]