A non-linear function is one that doesn’t follow the requirements for a linear function. This means that it should abide by any of the following conditions

• It should be of a higher degree than 1 (have exponents higher than 1)
• Include operations that aren’t addition - e.g multiplication, division, etc

Examples

• $f(x) = x^2$
• $f(x, y) = x^3 + y^2$

References

• https://www.wikiwand.com/en/Nonlinear_system