## Precalculus (10th Edition)

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 not mirrored, is vertically shifted by $-1$, 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 E.