Chapter 7: Rational Algebraic Functions Section 7-11: Variation Functions

Objectives Given a real world situation: Determine which kind of variation function is a reasonable mathematical model. Find the particular equation for the function. Predict values of y or x.

Variation Functions A relatively simple type of function that is very useful as a mathematical model has an equation in which y is equal to a constant multiplied or divided by a power of x. These are called variation functions.

Examples of Variation Functions The following equations are types of variation functions:

Definition of Variation Functions If k and n are constants, then “ y varies directly with the n th power of x ” means: y = kx n And “ y varies inversely with the n th power of x ” means: y = k/x n

Notes: If n is a positive integer: Direct variation functions are special cases of polynomial functions (linear, quadratic) Inverse variation functions are special cases of rational algebraic functions. The equation y = kx n can be both direct and inverse (because n could be negative). The words “Varies directly with” mean