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

did this on edge. here's my response (and the sample response if mine doesnt work) <3

Explanation:
My response:

A linear function has a constant additive rate of change, while a nonlinear function does not. On a table, you can add the amounts from the dependent variable to determine whether or not there's a constant additive rate of change (the added amount will be the same every time) while with nonlinear functions on a table, the added amounts will be different. On a graph, there's a curve that's usually a way to see that the function isn't linear. Though, if it is, the graphed line will stay going up at a constant rate.

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.

Answer 2

As you can probably guess, or already know, a linear function produces a straight line graph. A nonlinear function has some bent curve.

In terms of a table, a linear function has x and y increase at the same rate. For example, if x increases by 1 each time, then y would increase by say 4 each time. This means the slope is 4/1 = 4.

In contrast, a nonlinear function table will not have y increase the same amount each time. Consider an exponential function that grows faster and faster as you move to the right. The gap between adjacent y values gets larger.