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: 44

Answer

x-intercept is at (-3,0) y-intercept is at (0, 2) Vertical asymptote: x = 1/2 Domain: (-∞, 1/2) U (1/2, ∞) Horizontal asymptote: y=-1/3 Range: (-∞, -1/3) U (-1/3, ∞) Graph is below

Work Step by Step

$r(x)=\frac{2x+6}{-6x+3}$ 2x + 6 = 0 x = -3 Thus, the x-intercept is at (-3,0) y-intercept is the ratio of the constants, which is 6/3 = 2 Thus, the y-intercept is at (0, 2) Vertical asymptotes are when the denominator is equal to 0 -6x + 3 = 0 x = 1/2 So, domain is from (-∞, 1/2) U (1/2, ∞) Horizontal asymptote is the ratio of the constants of the leading term (with equal degree) 2/-6 = -1/3 Thus, the horizontal asymptote is at y=-1/3 So the range is from (-∞, -1/3) U (-1/3, ∞)
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.