8-1 Inverse Variation
Objectives
To recognize and use inverse variation
To use joint and other variations
Lesson Vocabulary
- inverse variation
- combined variation
- joint variation
Among all rectangles with a given area, the longer the length of one side, the shorter the length of an adjacent side.
Essential Understanding If a product is constant, where the constant is positive, a decrease in the value of one factor must accompany an increase in the value of the other factor.
As an equation, direct variation has the form
Problem 1 Identifying Direct and Inverse Variations
Is the relationship between the variables a direct variation, an inverse variation, or neither? Write function models for the direct and inverse variations.
Think
How can you tell if the quantities vary directly or inversely? If the product of corresponding x- and y-values is constant, they vary inversely. If the ratio of corresponding x- and y-values is constant, they vary directly.
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x y 2 15 4 7.5 10 3 15 2 As x increases, y decreases. This might be an inverse relationship. A plot confirms that an inverse relationship is possible. Test to see whether xy is constant.
The product of each pair is 30, so
Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions