Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 5 - 5.2 - Logarithmic Functions and Their Graphs - 5.2 Exercises - Page 379: 69


Domain: $x\lt0$ or $(-∞,0)$ x-intercept: $(-1,0)$ $x=0$ (y-axis) is the vertical asymptote.

Work Step by Step

$g(x)=\ln(-x)$ Domain: $-x\gt0$ $x\lt0$ or $(-∞,0)$ x-intercept: $g(x)=\ln(-x)=0$ $e^{\ln(-x)}=e^0~~$ (Using the Inverse Property $e^{\ln x}=x$): $-x=1$ $x=-1~~$ So, the x-intercept point is $(-1,0)$ $\ln (-x)→-∞$ when $-x→0^+$, that is, when $x→0^-$. Then $x=0$ (y-axis) is the vertical asymptote.
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