Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 13 - Section 13.4 - Nonlinear Inequalities and Systems of Inequalities - Exercise Set - Page 953: 15

Answer

Please see the graph.

Work Step by Step

$y^2/4 - x^2 \le 1$ This graph is for a hyperbola, and we have three regions to test (for different values of $y$): $(-∞, -2]$, $[-2, 2]$, and $[2, ∞)$. We can use the same $x$ value for the three chosen values of $y$ to test. Points to use to test: $(0, -3)$, $(0,0)$, $(0,3)$ $(0,-3)$ $y^2/4 - x^2 \le 1$ $(-3)^2/4 - 0^2 \le 1$ $9/4 -0 \le 1$ $9/4 \le 1$ (false) $(0,0)$ $y^2/4 - x^2 \le 1$ $0^2/4 - 0^2 \le 1$ $0/4 - 0 \le 1$ $0-0 \le 1$ $0 \le 1$ (true, so we shade the region with this point) $(0,3)$ $y^2/4 - x^2 \le 1$ $(3)^2/4 - 0^2 \le 1$ $9/4 -0 \le 1$ $9/4 \le 1$ (false)
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.