Question 802403
A piecewise function is a function that has more than one section to it, like if you combined different spliced different functions together at a certain point. 

In this problem, the first function ({{{y = 19.247 + 1.204t}}}) is graphed over the section where t is between -6 and -1 only. The second function ({{{y = 19.305 + 0.496t + 0.0116t^2}}}) is then graphed over its own section (from 0 to 13) on the t-axis (x-axis). 

This function tells you the average price of a home in a given year, t, and it wants to know how much it would be in the specific year, 1978. When they tell us that t=0 represents 1980, that gives us a frame of reference. So now we know that t=1 would be the next year, 1981; t=2 would be 1982; and so on. We can use this to work backwards as well. So t=-1 would be 1979, and t=-2 would be 1978. 

Now we have information that will be used in answering the question: t=-2 (for 1979), and the function that is applicable to the position t=-2 ({{{y = 19.247 + 1.204t, -6<t<-1}}}) because -2 is between -1 and -6, so this is the "piece" of our piecewise function that we use. 

Plugging -2 into {{{y = 19.247 + 1.204t}}}, we get {{{y = 19.247 + 1.204(-2) = 16.839}}}, which is our answer in thousands of dollars. So there you have it, the average price of a mobile home in '78 was $16,839.