Definition
Nonlinear function
A nonlinear function does not keep one constant rate of change across its whole domain.
Continue from this idea into connected AXIO math.
What it means
Take equal-sized steps in the input. A linear function changes its output by the same amount each time. A nonlinear function changes by different amounts somewhere, so its whole graph is not one straight line.
Remember it
Same input steps, changing output jumps.
Example
For N(x) = x², the inputs 0, 1, 2, 3 give outputs 0, 1, 4, 9. The output changes are +1, +3, +5. Because those equal input steps do not give equal output changes, N is nonlinear.
Watch for
A graph may contain a short straight piece and still be nonlinear overall. To be linear, the entire function must fit one straight-line rule on its domain.
Common mix-up
Nonlinear does not mean random. A nonlinear function can follow an exact rule, such as x², even though its rate of change is not constant.
Exact meaning
A nonlinear function is a function that cannot be represented by one rule of the form y = mx + b over its entire domain. Equal changes in input therefore do not always produce equal changes in output.