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: 70

Answer

Domain: $x\lt3$ or $(-∞,3)$ x-intercept: $(2,0)$ $x=3$ is the vertical asymptote.

Work Step by Step

$f(x)=\ln(3-x)$ Domain: $3-x\gt0$ $-x\gt-3$ $x\lt3$ or $(-∞,3)$ x-intercept: $f(x)=\ln(3-x)=0$ $e^{\ln(3-x)}=e^0~~$ (Using the Inverse Property $e^{\ln x}=x$): $3-x=1$ $-x=-2$ $x=2~~$ So, the x-intercept point is $(2,0)$ $\ln (3-x)→-∞$ when $3-x→0^+$, that is, when $-x→-3^+$, or when $x→3^-$. Then $x=3$ is the vertical asymptote.
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