College Algebra (10th Edition)

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

Chapter 6 - Section 6.4 - Logarithmic Functions - 6.4 Assess Your Understanding - Page 450: 115

Answer

The domain is $(-\infty,0)\cup(0, \infty)$. The range is $(-\infty,\infty)$. The x-intercepts are (-1,0) and (1,0). There are no y-intercepts.

Work Step by Step

The domain is a horizontal span from the function's smallest value of x to the function's largest value of x. If there is a discontinuity, the domain must show where the discontinuity happens. The range is a vertical span from the function's smallest value of f(x) to the function's largest value of f(x). If there is a discontinuity, the range must show where the discontinuity happens. The x-intercepts are all points of a graph when f(x)=0 while the y-intercepts are all points of a graph when x=0. In this case, there are only the x-intercepts: $0=ln(-x_1)$ $e^0=-x_1$ $1=-x_1$ $x_1=-1$ $0=ln(x_2)$ $e^0=x_2$ $x_2=1$
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