Siera calculated her home town'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 (2)
The function C ( F ) converts Fahrenheit to Celsius.
F represents the temperature in degrees Fahrenheit.
C ( F ) represents the equivalent temperature in degrees Celsius.
Therefore, C ( F ) is the output in degrees Celsius when F is the input in degrees Fahrenheit. The answer is C ( F ) represents the output of the function C in degrees Celsius when the input F is in degrees Fahrenheit.
Explanation
Understanding the Function The problem provides a function C ( F ) = 9 5 ( F − 32 ) that converts a temperature F in degrees Fahrenheit to degrees Celsius. We need to determine what C ( F ) represents.
Interpreting the Function Output The function C ( F ) takes a temperature in degrees Fahrenheit as input, which is represented by F . The function then outputs the equivalent temperature in degrees Celsius. Therefore, C ( F ) represents the temperature in degrees Celsius that corresponds to the input temperature in degrees Fahrenheit.
Final Answer Therefore, C ( F ) represents the output of the function C in degrees Celsius when the input F is in degrees Fahrenheit.
Examples
Imagine you're a weather forecaster in a country that uses Celsius, but you receive temperature data in Fahrenheit from a neighboring country. Using the conversion function C ( F ) = 9 5 ( F − 32 ) , you can easily convert the Fahrenheit temperatures to Celsius to inform your local audience. For example, if the data says the temperature is 77°F, you can calculate C ( 77 ) = 9 5 ( 77 − 32 ) = 9 5 ( 45 ) = 25° C . This allows you to provide accurate and understandable weather reports to the public.
The function C ( F ) converts temperatures from degrees Fahrenheit to degrees Celsius. Therefore, C ( F ) represents the output of the function in degrees Celsius when the input is in degrees Fahrenheit, making option A the correct choice. Option A states that C ( F ) is the output of the function C in degrees Celsius when the input F is in degrees Fahrenheit.
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