Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 3 - Review - Concept Check - Page 319: 14

Answer

(a) 1. move all items to one side; 2. factorize both the numerator and the denominator; 3. list all cut points; 4. build a sign table; 5. check endpoints and make conclusions based on the table. (b) Cut points separate regions of the function where the signs may change. To solve a rational inequality, use cut points to build up a sign table where the signs of the function are evaluated, see answer (a) for details. (c) $[-1,9]$

Work Step by Step

(a) Explain how to solve a polynomial inequality. 1. move all items to one side; 2. factorize both the numerator and the denominator; 3. list all cut points; 4. build a sign table; 5. check endpoints and make conclusions based on the table. (b) What are the cut points of a rational function? Explain how to solve a rational inequality. Cut points separate regions of the function where the signs may change. To solve a rational inequality, use cut points to build up a sign table where the signs of the function are evaluated, see answer (a) for details. (c) $f(x)=x^2-8x-9=(x-9)(x+1)\leq0$, cut points $-1,9$, make a table as shown and we conclude the solution as $[-1,9]$
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