Often in economics a linear function cannot explain the relationship between variables. In such cases a non-linear function must be used. Non-linear means the graph is not a straight line. The graph of a non-linear function is a curved line. A curved line is a line whose direction constantly changes.
A cautionary note: Economists are accustomed to designate all lines in graphs as curves - both straight lines and lines which are actually curved.
Although the slope of a linear function is the same no matter where on the line it is measured, the slope of a non-linear function is different at each point on the line. Thus there is no single slope for a non-linear function. However the slope can be determined at any point on the line. The techniques of differential calculus are used to determine the slopes of non-linear functions.
Three non-linear functions commonly used in economics are