Stitz-Zeager_College_Algebra_e-book

To that end we examine g f x 2 x2 4x 3 to keep

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Unformatted text preview: (x) = 1 − y 7 6 5 4 3 2 1 −6 −5 −4 −3 −2 −1 −1 −2 −3 −4 −5 1 2 3 4 5 6 x 5 x 266 Rational Functions −2x + 1 1 = −2 + x x 1 Shift the graph of y = x down 2 units. y (c) h(x) = 1 −3 −2 −1 1 2 3 x −1 −2 −3 −4 −5 y 3x − 7 1 =3− x−2 x−2 1 Shift the graph of y = x to the right 2 units. (d) j (x) = Reflect the graph of y = about the x-axis. Shift the graph of y = − up 3 units. 7 6 5 1 x−2 4 3 1 x−2 2 1 −3 −2 −1 1 −1 2 3 4 5 x 4.3 Rational Inequalities and Applications 4.3 267 Rational Inequalities and Applications In this section, we use sign diagrams to solve rational inequalities including some that arise from real-world applications. Our first example showcases the critical difference in procedure between solving a rational equation and a rational inequality. Example 4.3.1. 1. Solve x3 − 2x + 1 1 = x − 1. x−1 2 2. Solve x3 − 2x + 1 1 ≥ x − 1. x−1 2 3. Use your calculator to graphically check your answers to 1 and 2. Solution. 1. To solve the equation, we clear denominators x3 − 2x + 1 x−1 x3 − 2x + 1 · 2(x − 1) x−1 2x3 − 4x + 2 2x3 − x2 − x x(2x + 1)(x − 1) x = = = = = = 1 x−1 2 1 x − 1 · 2(x − 1) 2 x2 − 3x + 2 expand 0 0 factor − 1 , 0, 1 2 Since we cleared denominators, we need to check...
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