Answer
C
Work Step by Step
The function is $y=-\tan x$. In the general equation $y=a\tan bx$, when $a\lt0$, the graph is reflected across the x-axis.
In addition, comparing $y=-\tan x$ to $y=a\tan bx$, we find that $b=1$. The value of $b$ can be used to find the location of the two vertical asymptotes:
$bx=-\frac{\pi}{2}$ and $bx=\frac{\pi}{2}$
$1x=-\frac{\pi}{2}$ and $1x=\frac{\pi}{2}$
$x=-\frac{\pi}{2}$ and $x=\frac{\pi}{2}$
The location of the asymptotes is the same as that of the graph of $\tan x$.
Therefore, using this information, we can ascertain that the graph of $y=-\tan x$ will be the same as the graph of $y=-\tan x$ except that it will be reflected across the x-axis. This means that the correct graph for $y=-\tan x$ is C.
