Algebra and Trigonometry 10th Edition

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

Chapter 5 - Review Exercises - Page 413: 55


Domain: $x\gt6$ or $(6,∞)$ x-intercept: $(7,0)$ Then $x=6$ (y-axis) is the vertical asymptote.

Work Step by Step

$h(x)=\ln(x-6)$ Domain: $x-6\gt0$, that is, $x\gt6$ or $(6,∞)$ x-intercept: $h(x)=\ln(x-6)=0$ $e^{\ln(x-6)}=e^0$ (Using the Inverse Property $e^{\ln x}=x$): $x-6=1$ $x=7~~$So, the x-intercept point is $(7,0)$ $\ln(x-6)→−∞$ when $x-6→0^+$, that is, when $x→6^+$. Then $x=6$ (y-axis) is the vertical asymptote.
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