Question

Willis analyzed the following table to determine if the function it represents is linear or non-linear. First he found

he differences in the y-values as 7-1=6, 17-7= 10, and 31-17 = 14. Then he concluded that since the
Eifferences of 6, 10, and 14 are increasing by 4 each time, the function has a constant rate of change and is
near. What was Willis's mistake?
X
1
2
3
4
y
1
7
17
31
O He found the differences in the y-values as 7-1=6, 17-7= 10, and 31-17 = 14.
He determined that the differences of 6, 10, and 14 are increasing by 4 each time.
O He concluded that the function has a constant rate of change.
O He reasoned that a function that has a constant rate of change

Answer 1

Willis's mistake is assuming that a constant difference in the y-values implies a constant rate of change, which is not necessarily true for non-linear functions.

While it is true that a linear function will always have a constant rate of change, the converse is not true. A non-linear function can also have a constant difference in the y-values over a certain interval, but the rate of change is not constant. This is because the rate of change of a non-linear function varies at different points along the curve.

In this case, Willis did not consider the possibility of a non-linear function with a constant difference in the y-values. Therefore, his conclusion that the function is linear based on the constant differences in the y-values is not necessarily correct. To determine whether the function is linear or non-linear, Willis should have examined the differences in the x-values as well, or plotted the points on a graph to see if they lie on a straight line.