## Functions of one variable

Functions arise naturally in the study of economic problems. For example, a de-

mand function relates quantity demanded to price. Properties of such functions

are routinely studied – the slope and elasticity measure responsiveness of demand

to price variations. The techniques presented here introduce the tools required for

such calculations. Section 5.2 describes a variety of functions arising in different

areas (taxation, finance and present value calculations). Section 5.3 introduces

the basic notions of continuity and differentiability of a function. Certain families

of functions, such as logarithmic, polynomial and exponential functions, appear

frequently in economic applications; some of these are introduced in Section 5.4

and their shapes described. Growth rates and the algebra of growth calculations

are developed in Section 5.5. Finally, Section 5.6 provides rules for the differenti-

ation where the function is itself formed from other functions (such as the ratio or

product of functions).