Algebra and Trigonometry 10th Edition

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

Chapter 5 - Chapter Test - Page 415: 10

Answer

Domain: $x\gt4$ x-intercept: $(5,0)$ $x=4$ is the vertical asymptote.
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Work Step by Step

$f(x)=\ln(x-4)$ Domain: $x-4\gt0$ $x\gt4$ x-intercept: $f(x)=\ln(x-4)=0$ $x-4=e^0$ $x-4=1$ $x=5~~$ So, the x-intercept point is $(5,0)$ $\ln x \to\infty$ when $x\to0^+$. So: $\ln(x-4) \to\infty$ when $x-4\to0^+$ $\ln(x-4) \to\infty$ when $x\to4^+$ Thus, $x=4$ is the vertical asymptote.
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