Review of Functions

Business Calculus · Axiom Academy

A quick refresher on function concepts you'll need for business calculus A function is a rule that assigns exactly one output to each input. In business contexts, functions model relationships between quantities. A function f is a rule that assigns to each element x in a set D (the domain ) exactly one element f(x) in a set (the range ). In business calculus, you'll work primarily with these four types of functions: Constant rate of change. Used for simple cost models, depreciation. Creates a parabola. Used for revenue, profit optimization. Growth/decay by percentage. Used for compound interest, population. Inverse of exponential. Used for solving for time, diminishing returns. Each function type has a characteristic shape that helps us understand its behavior: The shape of a function tells us about its rate of change . Linear functions change at a constant rate. Exponential functions change faster and faster (or slower and slower). This is exactly what calculus helps us analyze precisely! In business problems, the domain is often restricted by practical constraints: Quantity must be non-negative: x 0 Quantity may have an upper bound: 0 x A company's cost function is C(x) = 500 + 25x where x is units produced. Domain: x 0 (can't produce negative units) Practical domain: 0 x 1000 (factory capacity) Range: C(x) 500 (fixed costs exist even at x = 0 ) In business, we often combine functions to create new ones: The most important function combination in business calculus:

This is the written version of the interactive lesson above. See the full Business Calculus course.