The thermostat in an empty apartment is set to \(65^\circ \text{F}\) from 4:00 a.m. to 5:00 p.m. and to \(50^\circ \text{F}\) from 5:00 p.m. until 4:00 a.m. Here is a graph of the function \(H\) that gives the temperature \(H(x)\) in degrees Fahrenheit in the apartment \(x\) hours after midnight.

Graph of function \(y = H(x), x y\)  plane, origin \(O\). Horizontal axis scale 0 to 22 by 2’s. Vertical axis scale 45 to 80 by 5’s. Function H starts at (0 comma 50) and is horizontal to (4 comma 50), then rises to (6 comma 65) and is horizontal to (17 comma 65). The function then drops to (19 comma 50) and is horizontal to (24 comma 50).

1. The owner of the apartment decides to change to a new schedule and sets the thermostat to change 3 hours later in the morning and the evening. On the same axes, sketch a graph of the new function, \(G\), giving the temperature as a function of time.
2. Explain what \(H(6.5) = 65\) means in this context. Why is this a reasonable value for the function?
3. If \(H(6.5) = 65\), then what is the corresponding point on the graph of \(G\)? Use function notation to describe the point on the graph of \(G\).
4. Write an expression for \(G\) in terms of \(H\).