Question

A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees.


Which best describes why the function is nonlinear?

The rate of change between 1 and 2 trees is different than the rate of change between 2 and 3 trees.
The rate of change between 1 and 2 trees is different than the rate of change between 1 and 3 trees.
The rate of change between 2 and 3 trees is different than the rate of change between 3 and 4 trees.
The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

Answer 1

The first choice. For a function to be nonlinear, the rate of change must vary on equal-length intervals. The rate from 1→2 trees differs from the rate from 2→3 trees, so the function is nonlinear.