Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - 1.2 Representing Functions - 1.2 Exercises - Page 21: 15


The function is $$f(x)=-\frac{3}{50}x+27;$$ The domain is $(0,450)$; The graph is on the figure below

Work Step by Step

Let $x$ denote the price in USD of Blu-ray players and $y$ average units sold per day. Then this linear function passes through points $P(200,15)$ and $Q(250,12)$. Then the equation of this linear function is given $$y=\frac{12-15}{250-200}(x-200)+15=-\frac{3}{50}x+\frac{3}{50}\cdot 200+15=-\frac{3}{50}x+27,$$ so the required function is $$f(x)=-\frac{3}{50}x+27.$$ Considering that the price should be positive and that the number of sold units should be positive as well, the domain is determined by $x>0$ and $f(x)>0\Rightarrow-\frac{3}{50}x+27>0\Rightarrow x<450.$ Finally the domain is $$\mathcal{D}=(0,450).$$ The graph is the line passing through points $P$ and $Q$.
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