College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 5 - Systems of Equations and Inequalities - Exercise Set 5.5 - Page 571: 25


please see image .

Work Step by Step

1. The inequality sign is $\geq $, so we draw a solid border 2. The border, $y=\log_{2}(\mathrm{x}+1)$ is a logarithmic function, base $2 > 1,$ It is obtained from $\log_{2}x$ by shifting left by one unit. The function is defined only for $x>-1.$ This means that its vertical asymptote, $x=-1$ will not be included in the solution, and will be a border. We graph it with a dashed line (not included). Plot some points (see table) and join with a smooth (solid) curve 3. We can't test the point $(0,0)$, as it lies on the border curve. We test (1,0) $ 0 \geq \log_{2}(1+1)\quad ?$ $0 \geq \log_{2}2\quad ?$ $0 \geq 1\quad ?$ No. 4. Shade the region that the point (1,0) does not belong to. Also, apply the observation about the vertical asymptote (we shade the region to the right of the asymptote)
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