Activity 1.6.3.
Let \(F = D(N) = 40 + 0.25N\) be Dolbear’s function that converts an input of number of chirps per minute to degrees Fahrenheit, and let \(C = G(F) = \frac{5}{9}(F-32)\) be the function that converts an input of degrees Fahrenheit to an output of degrees Celsius.
(a)
Determine a formula for the new function \(H = (G \circ D)\) that depends only on the variable \(N\text{.}\)
(b)
What is the meaning of the function you found in (a)?
(c)
How does a plot of the function \(H = (G \circ D)\) compare to that of Dolbear’s function? Sketch a plot of \(y = H(N) = (G \circ D)(N)\) on the blank axes to the right of the plot of Dolbear’s function, and discuss the similarities and differences between them. Be sure to label the vertical scale on your axes.
(d)
What is the domain of the function \(H = G \circ D\text{?}\) What is its range?
