The standard model for a linear function is Ax + By + Cz = D, where A, B, C and D are constants and x, y and z are variables. There can be any number of constant-variable terms, and any equation that can be manipulated into this form is also a linear function. Linear functions are often encountered in systems of several linear functions. For example, if five men and three women register 1,260 lbs. in the elevator sensor and four men and six women register 1,440 lbs., we have two linear equations. There are techniques for solving systems of linear equations that can be used to show that the average weight of men is 180 lbs. and the average weight of women is 120 lbs.
The most common of the non-linear functions are polynomial. Variables may be multiplied by constants and raised to powers and these terms may be added together. The model of a polynomial function if y = Ax^3 + Bx^2 + Cx + D. There may be more or fewer terms and there may be more than two variables. Polynomials become infinite when the values of the variables are large -- they never become infinite in the middle of the graph, only at the extremely left and right sides. The graphs are curves that may change direction several times.
Rational function are not more logical than other functions -- the name comes from the word "ratio." Rational functions have variables in denominators. The graphs are curves and also have asymptotes. These are invisible lines that the graph will approach closer and closer as the values of the curve becomes infinite. Asymptotes appear in the places where the denominator becomes zero.
All trigonometrical functions are non-linear. The sine and cosine functions look very similar -- one is identical with the other only shifted 90 degrees to the left or right. They are models of what we think of a radio or electricity waves. In fact, the name for these type waves is "sinusoidal." They have no asymptotes and are periodic -- they repeat the same form over and over endlessly. The other four trigonometric functions are also periodic with asymptotes every 180 degrees.