Function arithmetic and algebra deals with manipulating functions using the usual arithmetic of numbers. You may recall that arithmetic operations on numbers include sum, difference, multiplication, division and exponentiation. A particularly important computation required in calculus is that of the difference quotient of a function (also known by slope of a line, average rate of change, etc.) over an interval. In addition to these operations, we also learn about composition of two or more functions in a later section.
The result of arithmetic operations on functions is again a function. So naturally we would be particularly interested in the domain of the resulting function which in turn depends on the individual functions.
- Function arithmetic - Sum, Difference, Product, and Quotient
- Composition of Functions
- Domain of Resulting Function
- Difference Quotient for polynomials, rational functions and nth-root functions.
- Examples of functions in practice -
- Position function of a projectile
- Compound Interest
- Volume of Regular objects (cylinder, cone, sphere)
Price-Demand, Revenue Cost, Average Cost and Profit function