Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.3 - Logarithmic Functions - 4.3 Exercises - Page 352: 69

Answer

Domain :$\qquad(1,+\infty)$ Range :$\qquad(-\infty,+\infty)$ Vertical asymptote: $\qquad x=1$

Work Step by Step

We start with the graph of $f_{1}(x)=\log_{3}(x)$ (dashed blue). Since y$=\log_{3}(x-1)-2=f(x-1)-2$ its graph (red) is obtained by 1. shifting $f_{1}(x)$ right by 1 units (green dotted), 2. then shifting down by 1 units. Domain :$\qquad(1,+\infty)$ Range :$\qquad(-\infty,+\infty)$ Vertical asymptote: $\qquad x=1$
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