Stitz-Zeager_College_Algebra_e-book

Solve each rational inequality express your answer

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Unformatted text preview: on gives us 2 x4 + 1 = x2 − 1 + 2 2+1 x x +1 The remainder is not zero so r(x) is already reduced. 3. To find the x-intercept, we’d set r(x) = 0. Since there are no real solutions to have no x-intercepts. Since r(0) = 1, so we get (0, 1) for the y -intercept. x4 +1 x2 +1 = 0, we 4. This step doesn’t apply to r, since its domain is all real numbers. 5. For end behavior, once again, since the degree of the numerator is greater than that of the denominator, Theorem 4.2 doesn’t apply. We know from our attempt to reduce r(x) that we can rewrite r(x) = x2 − 1 + x22 , and so we focus our attention on the term corresponding +1 to the remainder, x22 It should be clear that as x → ±∞, x22 ≈ very small (+), which +1 +1 means r(x) ≈ x2 − 1 + very small (+). So the graph y = r(x) is a little bit above the graph of the parabola y = x2 − 1 as x → ±∞. Graphically, y 5 4 3 2 1 x 14 But rest assured, some graphs do! 258 Rational Functions 6. There isn’t much work to do for a sign diagram for r(x), si...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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