# Non-Linear Functions

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

• the exponential function
• the quadratic function
• the logarithmic function

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