Alg 2 BC U9Day 1 - Direct, Inverse, Combined & Joint Variation

DIRECT VARIATION: If "y varies directly as x", then ______, where "k" is a ______.

So, if "w varies directly as z" then: ______.

If "t varies directly as the square root of r", then: ______.

** If , then ______. **

Therefore, to test whether a set of points represents a direct variation, test each combination

to check if the value of is a constant (the same value for each pair).

INVERSE VARIATION: If "y varies inversely as x", then ______, where "k" is a ______.

So, if "w varies inversely as z" then: ______.

If "t varies inversely as r to the third", then: ______.

** If , then ______. **

Therefore, to test whether a set of points represents an inverse variation, test each combination

to check if the value of is a constant (the same value for each pair).

Determine whether each function represents a DIRECT VARIATION, an INVERSE VARIATION or neither.

If it does represent a variation, write the specific equation.

x / y
2 / 8
3 / 12
5 / 20

1. 2.

x / y
2 / 4
-1 / -8
.5 / 16

3. 4.

x / y
-6 / -2
3 / 1
12 / 4
x / y
-1 / -2
3 / 4
6 / 7

COMBINED and JOINT variation: combines direct and inverse variations in more complicated relationships

Examples:

Combined variation / Equation form
y varies directly with the square of x
y varies inversely with the cube of x
z varies jointly with x and y
z varies jointly with x and y and inversely with w
z varies directly with x and inversely with the product of w and y

Examples

1. Suppose that x and y vary inversely, and x=3 when y=-5. Write the function that models the inverse variation.

2. Suppose that x and y vary inversely, and x=0.3 when y=1.4. Write the function that models the inverse variation.

11. Newton’s Law of Universal Gravitation is modeled by the formula . F is the gravitational force between two objects with masses, m1 and m2, and d, the distance between the objects. G is the gravitational constant. Describe Newton’s Law as a combined variation.

For homework: Do Page 481-482: 1-55 odd