The graph, $G$ of $y=\log_{10}x$ is rotated $90^{\circ}$ counter-clockwise about the origin to obtain a new graph $G'$. Which of the following is an equation for $G'$?
(A) $y=\log_{10}\left(\frac{x+90}{9}\right)$ (B) $y=\log_{x}10$ (C) $y=\frac{1}{x+1}$ (D) $y=10^{-x}$ (E) $y=10^x$
$\fbox{D}$ Rotating a point $(x,y)$ $90^{\circ}$ anticlockwise about the origin maps it to $(-y,x).$ (You can prove this geometrically, or using matrices if you aren't convinced). Thus $(x, \log_{10}x)$ maps to $(-\log_{10}x, x)$, so new $y =$ old $x = 10^{\log_{10}x} = 10^{-(-\log_{10}x)} = 10^{-\text{new} x}$, so the new equation is $y=10^{-x}.$