Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.4 Logarithmic Functions - 5.4 Assess Your Understanding - Page 295: 67



Work Step by Step

If a logarithmic function has a of: $y=\pm\log_a{(\pm x-c)}+b$, where $a\gt1$, then it is: (1) if the sign front of the $\log$ function is negative, it is vertically mirrored to the x-axis (2) vertically shifted by $b$ (compared to $y=\log_a{x}$) (3) horizontally shifted by $c$ (compared to $y=\log_a{x}$) and has a vertical asymptote at $x=c$ (4) if the sign front of $x$ is negative, it is horizontally mirrored to the vertical asymptote (compared to $y=\log_a{x}$) Here the graph is vertically mirrored, is vertically not shifted, has a vertical asymptote of $x=0$ and is horizontally mirrored compared to $y=log_3{x}$ (see in the picture). Hence the function is D.
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