CPMP Course 2, Unit 1, Lesson 1, Inv. 2 Power Function p.12

Use the sliders to explore the relationship between the power r, the constant of proportionality k, and the numerical patterns relating x and y. To see patterns that help answer this question, you might begin by studying examples in which k=1 and r= 1, 2, 3, 4, 5, and 6. Then explore what happens for positive and negative values of the proportionality constant k. Describe the patterns you observe.
Based on the calculations involved in the different rules used above, explain why the different observed patterns make sense.