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 :

The conversion function is given by

$$
C(n) = \frac{5}{9}(F - 32),
$$

where $F$ represents a temperature measured in degrees Fahrenheit, and $C(n)$ (or $C(F)$, since the function is being applied to $F$) gives the corresponding temperature in degrees Celsius.

Here is the step-by-step reasoning:

1. The function is defined as converting a temperature from the Fahrenheit scale to the Celsius scale.
2. In the formula, $F-32$ is calculated first, which adjusts the Fahrenheit temperature to account for the different zero points of the two scales.
3. Then, the result is multiplied by $\frac{5}{9}$, which scales the adjusted temperature to the Celsius value.
4. Therefore, when you input a temperature $F$ (in degrees Fahrenheit), the function $C$ outputs the temperature in degrees Celsius.

Thus, $C(F)$ represents the temperature, expressed in degrees Celsius, when the input $F$ is given in degrees Fahrenheit.

The correct answer is:

$$\textbf{1. } C(F) \text{ represents the output of the function } C \text{ in degrees Celsius when the input } F \text{ is in degrees Fahrenheit.}$$