Key Concepts Sect 9.1
Inverse Variation: A function defined by the equations xy = k, y = k/x, or x = k/y where k ≠ 0.
Constant of Variation: The value of k in the inverse variation equations.
Joint Variation: When a set of 3 or more variables are directly and/or inversely varying.
Guided Practice Sect 9.1
Ex 1: Suppose that x and y vary inversely, and x = 7 when y = 4. Write the function that models the inverse variation.
Guided Practice Sect 9.1
Ex 2: Is the relationship between the variables in each table a direct variation, an inverse variation, or neither? Write functions to model the direct and inverse variations.
c.)
b.)
a.)
x
x y x y y 2 0.7 ­2 6 ­2 5 4 0.35 ­1.3 5 4
­10 14 0.1 7 ­4 6 ­15 Ex 3: The pressure P of a sample of gas at a constant temperature varies inversely as the volume V. Use the data in the table to write a function that models this inverse variation. Use the equation to estimate the pressure when the volume is 6 in3.
Pressure Volume
(lb/in2) (in3) 3 32 5 19.2 8 12 Ex 4: The mass m of a moving object is related to its kinetic energy k and its velocity v by the formula m = 2k/v2. Describe the relationship as a combined variation. Homework
Sect 9.1: p.491
3, 6, 9, 10, 12­54 every 3rd,
66­72 every 3rd