Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall

Chapter 11 Graphing Quadratic Functions, Rational Functions, and Conic Sections

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall 11.8 Nonlinear Inequalities and Systems of Inequalities

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Nonlinear inequalities in two variables are graphed in a similar way to linear inequalities in two variables.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Sketch a dashed curve since the graph of does not include the graph of x y 4 – 4 – 3 3 Example continued

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Select a test point to determine which region contains the solutions. Select the test point (0, 0) if it is not on the boundary line. x y 4 – 4 – 3 3 This is a true statement, so the test point is part of the solution. (0, 0)

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Sketch a solid curve since the graph of does include the graph of x y – Example continued

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall The hyperbola divides the plane into three regions. Select a test point in each region to determine the solutions. Region A x y – (0, – 4 ) Region A (0, 4) (0, 0) Region B Region C False Region B True Region C False continued

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall The graph of the solution set includes the shaded region B only. It also includes the boundary lines. x y – 2 2 2

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall Graph each inequality on the same set of axes. Graph the system. x y – Example continued

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall x y – Shade the solution set for each inequality. The solution to the system is the dark area where both regions are shaded.