Ever since Year One we have worked with “functions” — the straight line, the parabola, the absolute value, radicals, the rational (homographic) function — but always treating them case by case, assigning to each a list of specific properties. In this chapter we take a step back and introduce the general language of functions: domain, codomain, image, injectivity, surjectivity, inverse function, monotonicity, concavity. It is a uniform terminology that lets us speak in the same way about all functions, old and new. The chapter closes with piecewise-defined functions and an economic application — demand, supply and market equilibrium — which shows how these ideas model real situations.
Sections
- Definition of a function
- Injectivity, surjectivity, bijectivity
- Inverse function
- Monotonicity
- Concavity and convexity
- Natural domain
- Piecewise-defined functions
- Application: demand, supply, market equilibrium