Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 3 - Section 3.6 - Rational Expressions - 3.6 Exercises - Page 309: 51

Answer

x-intercept: (2,0) y-intercept: (0, 2) Vertical Asymptote: x=-2, 1 Domain: (-∞, -2) U (-2, 1) U (1, ∞) Horizontal Asymptote: y=0 Range: (-∞, ∞) See graph below

Work Step by Step

$r(x)=\frac{2x-4}{x^2 + x -2}$ $2x-4 = 0$ x = 2 x-intercept: (2,0) y-intercept is the ratio of the constants, which is -4/-2 = 2 Thus, the y-intercept is at (0, 2) Vertical asymptotes are when the denominator is equal to 0 $x^2 + x -2 = 0$ $(x+2)(x-1) = 0$ x = -2, 1 So, domain is from (-∞, -2) U (-2, 1) U (1, ∞) Horizontal asymptote is the ratio of the constants of the leading term (with equal degree) 0 (since top degree is not 2, unlike bottom) Thus, the horizontal asymptote is at y=0 So the range is from (-∞, ∞)
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