How to determine if a function is linear or nonlinear?
Understand the Problem
The question is asking for the criteria or methods to identify whether a given function exhibits linear characteristics or nonlinear behavior. This includes understanding concepts such as the standard form of linear functions, the characteristics of their graphs, and how to analyze equations for linearity.
Answer
Check the graph, equation, or table of values.
To determine if a function is linear or nonlinear, you can check the graph for a straight line, the equation for the form y=mx+b, or the table of values for a constant rate of change.
Answer for screen readers
To determine if a function is linear or nonlinear, you can check the graph for a straight line, the equation for the form y=mx+b, or the table of values for a constant rate of change.
More Information
Linear functions are simpler as they only depend linearly on their input. Nonlinear functions can model more complex phenomena.
Tips
A common mistake is to assume a function is linear just because it appears straight over a small range. Always check the larger context or more values.
