Linear vs. Nonlinear Functions Answers

Look at the graph. Leslie analyzed the graph to determine if the function it represents is linear or non-linear. First she found three points on the graph to be (–1, –4), (0, -3), and (2, 5). Next, she determined the rate of change between the points (–1, –4) and (0, -3) to be and the rate of change between the points (0, -3) and (2, 5) to be . Finally, she concluded that since the rate of change is not constant, the function must be linear. Why is Leslie wrong?

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?xy1127317431

Carol is cross-country skiing. The table shows the distance she traveled after various numbers of minutes. What is the rate of change?Distance Carol Traveled while Cross-Country SkiingMinutesDistance Traveled (miles)23456

What is the rate of change of the function represented by the table?xy15253545