chapter 7: rational algebraic functions section 7-11: variation functions
TRANSCRIPT
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
#1 and 3