Every quantitative model — from the price of a European call to a mean-reverting interest rate — is ultimately a function: a rule that assigns an output to each input. This topic builds the vocabulary you need before calculus begins: what a function is, how to describe one in four equivalent ways, which families of functions recur across finance and science, and how to manufacture new functions from old ones by shifting, scaling, composing, and inverting.
The finance thread running through the topic is compounding. By the end of Lesson 3 you will have derived the natural exponential from the discrete compounding limit — the same limit that forces to appear in the Black-Scholes formula, bond pricing, and every continuous-time model you will meet in later units.
By the end of this topic you should be able to:
- state and apply the four representations of a function (verbal, numerical, visual, algebraic) and move fluently between them;
- identify the class a function belongs to (linear, polynomial, rational, power, exponential, trigonometric) from its formula or graph;
- apply the six families of graph transformation (vertical/horizontal shift, vertical/horizontal stretch, reflection) to sketch a new graph from a known one;
- form sums, products, quotients, and compositions of functions and determine their domains;
- derive from the continuous-compounding limit and state its numerical value;
- find and graph the inverse of a one-to-one function; compute and use logarithm laws.
In this lesson
- Contents
- The big picture
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