Chapter 9.2, Problem 50E

Calories and temperature Suppose that the number of calories of heat required to raise 1 g of water (or ice) from $\text{- 40°C to }x\text{°C}$ is given by

$f(x)=\{\begin{array}{l}\frac{1}{2}x+20\text{ if -40}\le <0\\ x+100\text{ if 0}\le x\end{array}$

(a) What can be said about the continuity of the function f(x)?

(b) What happens to water at $\text{0°C}$ that accounts for the behavior of the function at $\text{0°C}$?