Functions

Functions describe how one quantity depends on another, forming the central concept of precalculus and calculus. This topic covers determining domain and range, composing functions, finding inverses, working with exponential functions, and analyzing piecewise-defined functions.

Functions model virtually every quantitative relationship in science and economics, from population growth (exponential functions) to tax brackets (piecewise functions) to cryptographic encoding (composition and inverses).

Practice Tips

• 1To find the domain, identify values that cause division by zero or negative values under even roots, then exclude them.
• 2When composing f(g(x)), substitute the entire expression for g(x) into f, then simplify; pay close attention to the order.
• 3To find an inverse function, swap x and y in the equation and solve for y, then verify by checking that f(f inverse(x)) = x.