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?
Answer
A
The points (–1, –4), (0, –3), and (2, 5) are not all on the graph.
B
The expressions and both equal 1.
C
She miscalculated the rates of change.
D
Her conclusion is wrong. If the rate of change is not constant, then the function cannot be linear.