Question

The values of x and f(x) for a function are shown in the table below.





x f(x)
0 3
1 6
2 12




Which statement below is correct about the rate of change of the function over this interval?




The rate of change from x = 0 to x = 1 is greater than the rate of change from x = 1 to x = 2.


The rate of change from x = 0 to x = 1 is less than the rate of change from x = 1 to x = 2.


The rate of change does not change at different intervals.


The rate of change is decreasing from x = 0 to x =
∞
.

Answer 1

The rate of change from 0 to 1 is (6−3)/(1−0) = 3, and from 1 to 2 is (12−6)/(2−1) = 6. So the rate of change from x = 0 to 1 is less than the rate from x = 1 to 2.