Question

http://media.education2020.com/evresources/3108-01-07/mc017-1.jpg
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, –1), (0, 0), and (1, 1). Next, she determined the rate of change between the points (–1, –1) and (0, 0) to be 0-(-1)/0-(-1)=1/1=1 and the rate of change between the points (0, 0) and (1, 1) to be 1-0/1-0=1/1=1 . Finally, she concluded that since the rate of change is constant, the function must be linear. Why is Leslie wrong?

Answer 1

@crazysingh

Answer 2

she can not calculate rate of change of y with respect to x with this method. that method is which she used is only applicable for linear function. for other function she will have to use differentiation.

linear function looks like a straight line. but it is not. you can see the graph.

Answer 3

oh wait sorry i didnt post the multiple choices
A:The points (–1, –1), (0, 0), and (1, 1) are not all on the graph.
B:The expressions mc017-4.jpg and mc017-5.jpg do not both equal 1.
C:The rate of change between the points (–1, –1) and (0, 0) is not constant, nor is the rate of change between the points (0, 0) and (1, 1).
D:The rate of change of a linear function is not constant.