Chapter 7:Rational Algebraic

FunctionsSection 7-11:

Variation Functions

ObjectivesGiven 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 FunctionsA 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:

24y x

13y

x

2

0.732y

x

1.9y x

Definition of Variation Functions

If k and n are constants, then “y varies directly with the nth power of x” means:

y = kxn

And “y varies inversely with the nth power of x” means:

y = k/xn

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 = kxn can be both direct and inverse (because n could be negative).The words

“Varies directly with” mean

HOMEWORK:p. 391

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