Exploration of Inverse Functions

Exploration of Inverse Functions

By Richard Getzel

​There are two functions graphed above. One represents the conversion formula for degrees Celsius to degrees Fahrenheit. The other represents the conversion formula for degrees Fahrenheit to degrees Celsius.

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Fahrenheit as a Function of Celsius and Vice Versa

Multiple Choice

Which formula would you use to convert 10 degrees Celsius (the independent variable) into its equivalent in Fahrenheit (the dependent variable)?

• $$y\ =\ \frac{9}{5}x\ +\ 32$$  

• $$y=\frac{5}{9}\left(x-32\right)$$  

Open Ended

These two formulas are examples of inverse functions. Based on your observations of their graphs, speculate on what relationships might exist between these two equations (visually, algebraically, or otherwise).