Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.8 - Modeling Using Variation - Exercise Set - Page 425: 51

Answer

The provided statement makes sense.

Work Step by Step

Variation formulas are the formulas that define the relation between two quantities such that if one quantity varies, we will know how it affects another quantity. The direct variation equation can be defined as: $y=kx$ Here, quantity y varies directly as soon as x varies and k is known to be a constant of variation. Obviously, as shown above, the direct variation equation is certainly a special case of the linear function, since linear functions have the general form of: $y=kx+b$. Inverse variation equation can be defined as: $y=\frac{k}{x}$ This means that one quantity increases as the other decreases. It is said that y is inversely proportional to x because y varies inversely as x. k is called a constant of variation and $k\ne 0$. The inverse variation equation is a rational function because behavior of the inverse variation of a variable makes it the equation of rational variables. By definition, in rational functions, the general rational equation is described for rational variables. For example, $y=\frac{k}{x}+b$ is a general form of a rational equation.
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