Atown’s jobless rate can be modeled by (1, 3.3), (2, 4.9), (3, 5.3), (4, 6.4), (5, 4.5), (6, 5.6), (7, 2.5), (8, 2.7). how many turning points would the graph of a polynomial function through these points have?

Analyze the transition (or slope) between each adjacent pair of points. You can do this by first graphing the function, or by comparing the y values of adjacent points. 

#1 - From (1, 3.3) to (2, 4.9), the y values increase, so the slope is positive. 
#2 - From (2, 4.9) to (3, 5.3), the y values increase, so the slope is positive. 
#3 - From (4, 6.4) to (5, 4.5), the y values decrease, so the slope is negative. 
#4 - From (5, 4.5) to (6, 5.6), the y values increase, so the slope is positive. 
#5 - From (6, 5.6) to (7, 2.5), the y values decrease, so the slope is negative. 
#6 - From (7, 2.5) to (8, 2.7), the y values increase, so the slope is positive. 

Notice that there are four times when the slope changes polarity (between #2 and #3, between #3 and #4, between #4 and #5 and between #5 and #6). These are the turning points for this graph.