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 572: 45

Answer

The solution set is the region shaded GRAY .
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Work Step by Step

We will graph the solution region for each inequality. Quadratic functions have a parabola for a graph. To graph a line, we need two points...unless we know it is vertical or horizontal. 1. (red) Border:$\quad y=x^{2}-1\quad $solid line ( sign is $\geq )$, The curve is a parabola that opens up $(a=1>0)$ , with vertex: $(0,-1)$ x-intercepts: $0=x^{2}-1$ $0=(x+1)(x-1)$ x-intercepts:$ \quad \pm 1$ Testing $(0,0):\quad 0 \geq 0^{2}-1\quad?$ Yes, shade the region containing $(0,0)$ 2 (blue) $x-y=-1 \quad $solid line ( sign is $\geq )$, x-intercept:$\quad x-0=-1\quad$ point: ($-1,0)$ y-intercept:$ \quad 0-y=-1\quad$ point: ($0,1)$ Testing $(0,0)$:$\quad 0-0 \geq -1 \quad ?$ Yes, shade the region containing (0,0) The solution set is the region with BOTH shadings. The solution set is the region shaded GRAY
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