3.14

Topic

Polar Function Graphs Describe characteristics of the graph of a polar function. If a polar function, r = f ( ), is positive and increasing or negative and decreasing, then the distance between f ( ) and the origin is increasing. 3.15.A.2 If a polar function, r = f ( ), is positive and decreasing or negative and increasing, then the distance between f ( ) and the origin is decreasing. 3.15.A.3 For a polar function, r = f ( ), if the function changes from increasing to decreasing or decreasing to increasing on an interval, then the function has a relative extremum on the interval corresponding to a point relatively closest to or farthest from the origin. 3.15.A.4 The average rate of change of r with respect to over an interval of is the ratio of the change in the radius values to the change in over an interval of . Graphically, the average rate of change indicates the rate at which the radius is changing per radian. 3.15.A.5 The average rate of change of r with respect to over an interval of can be used to estimate values of the function within the interval.