Modeling Temperature Changes After Daylight Saving Time Shift
The image shows a line graph with the x-axis labeled "Hours" from 0 to 24 and the y-axis labeled "Temperature" from 50 to 90 degrees in increments of 10. The line graph itself indicates changes in temperature over the course of a day.
The accompanying text describes that during a month in a certain town, the temperature increases and decreases over the course of a day as shown in the graph. A particular point is mentioned where the temperature readjusts due to time change for daylight saving time. If the clock is adjusted forward by one hour at 1 a.m., then what was originally 1 a.m. instantaneously becomes 2 a.m. The question stipulates that if we have a function T for temperature with respect to hours, we are seeking a function D that models the same data, considering the time shift for daylight saving time.
To solve for function D in terms of function T after the time shift, if the function T(h) represents the temperature at hour h, then for the time after the time shift, we need to subtract one hour from the h values because the clock jumps forward one hour (i.e., what was 1 a.m. becomes 2 a.m.). Therefore, the point on the graph that was originally at T(h) is now at T(h-1) when h is after 1 a.m.
Thus, if we denote D(h) as the function for temperature after the time shift, we can define D(h) in terms of T as:
D(h) = T(h-1) for h > 1.
Remember that this adjustment is only applicable for hours after the time shift occurs. For the first hour (from midnight to 1 a.m.), there is no shift, so D(h) would equal T(h) within that interval. However, since the question does not ask for this specific interval and from the context of the question it is clear that we're only considering the hours after the daylight saving time change, the general solution for hours after 1 a.m. would be as stated above.
