College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 5 - Cumulative Review - Page 399: 15

Answer

(a) The domain is $(-\infty,1)\cap(1,\infty)$ (b) (2,6) is not on the graph. (c) f(x)=4 (d) x=1.75 (e) f(x) is a rational function.

Work Step by Step

(a) There is a vertical asymptote at x=1; therefore the domain is $(-\infty,1)\cap(1,\infty)$ (b) Let's find f(2) to see if it equals 6: $f(2)=\dfrac{2+5}{2-1}=\dfrac{7}{1}=7$ It doesn't, so (2,6) is not on the graph. (c) To find out, let's calculate f(3): $f(3)=\dfrac{3+5}{3-1}=\dfrac{8}{2}=4$ (d) To find out, let's replace f(x) with 9 and solve for x: $9=\dfrac{x+5}{x-1}$ $9\cdot (x-1)=\dfrac{x+5}{x-1}\cdot (x-1)$ $9x-9=x+5$ $9x-x-9+9=x+5-x+9$ $8x=14$ $x=\frac{14}{8}=1.75$ (e) Polynomial functions don't have negative degrees, while rational functions do; therefore, f(x) is a rational function.
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