Direct variation: A linear function defined by an equation ...
Alg 2 BC U9 Day 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 [pic], then [pic]_____________. **
Therefore, to test whether a set of points represents a direct variation, test each combination
to check if the value of [pic]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 [pic], then [pic]_____________. **
Therefore, to test whether a set of points represents an inverse variation, test each combination
to check if the value of [pic]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 [pic]. 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
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Direct variation: A linear function defined by an equation of the form [pic] or [pic], where k is called the constant of variation and [pic].
Inverse Variation: A function of the form [pic] or [pic]
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