Question

What is the difference between a linear function and a nonlinear function? Explain what each looks like when represented as a table and as a graph.

Answer 1

The difference between the linear and nonlinear functions are their degrees. For linear functions, the highest order is only 1 while more than for those nonlinear functions. If these are presented in graphs, linear functions would generate straight lines while parabola or other curved lines will be generated for nonlinear functions. 

Answer 2

The correct answer is:

A linear function has a constant rate of change, while a non-linear function does not have a constant rate of change.

Explanation:

As the name implies, a linear function will graph as a straight line. Since it is a straight line, this means that the distance between any two consecutive points must be the same; it must go up or down the same amount between each pair of points, or it will not form a straight line.

This means that a table of a linear function will have consecutive values that either increase or decrease by the same amount.

A non-linear function, on the other hand, will not have these things. It will not graph as a straight line, and each pair of consecutive points will not increase or decrease by the same amount. Instead, they will increase or decrease by different amounts.

Answer 3

Sample Response: A linear function has a constant additive rate of change, while a nonlinear function does not. For a table of values to be linear, the dependent variable must have a constant rate of change as the independent variable increases by 1. On a graph, the function must be a straight line to be linear.