Question

Willis analyzed the following table to determine if the function it represents is linear or non-linear. First he found the differences in the y-values as 7 – 1 = 6, 17 – 7 = 10, and 31 – 17 = 14. Then he concluded that since the differences of 6, 10, and 14 are increasing by 4 each time, the function has a constant rate of change and is linear. What was Willis’s mistake?

Answer 1

He's subtracting y2 - y1 to obtain a difference. But the actual change in y is much larger than 4, and is different each time, so it can't be linear. Going from 1, to 7, to 17, to 31, is going to make one hell of a curve.