Celsius to Fahrenheit formula to calculate range of temperatures Let's assume the maximum temperature during a month is $86 F ^\circ$ of all days and the minimum temperature during a month of all days is $74 F ^ \circ $. The range of temperature is the difference of the two, so $12 F ^\circ$. The formula for the temperature is $$C=\frac{5}{9}(F-32)$$. Why isn't the corresponding range of temperature in that particular month in centigrade $$C=\frac{5}{9}(12-32)$$ but rather around $$7 C ^\circ$$?

That because the difference of two values of an _affine function_ is the value of the _associated linear map_ at the difference.

In formula: $$\bigl(a(x+\Delta x)+b\bigr)-(ax+b)=a\mkern 2mu\Delta x, \quad\text{not }\; a\mkern 2mu\Delta x+b.$$