Answer
Refer to the blue graph below.
Work Step by Step
The parent function of $y=\cos{(2x)}$ is $y=\cos{x}$.
Note that in $y=\cos{x}$, when $x$ is replaced by $2x$, the function becomes $y=\cos{(2x)}$
This means that with $y=f(x)=\cos{x}$ as the parent function, the given function is equivalent to $y=-f(2x)$
RECALL:
(i) The graph of $y=f(cx)$ involves a horizontal shrink by a factor of $c$of the parent function $y=f(x)$.
(ii) The graph of $f=-f(x)$ involves a reflection about the $x$-axis of the parent function $y=f(x)$.
Thus, to graph the given function, perform the following steps:
(1) Graph the parent function $y=\cos{x}$. Refer to the black graph below.
(2) Shrink the graph of the parent function horizontally by a factor to obtain the graph of $y=\cos{(2x1)}$. Refer to the green graph below.
(3) Reflect the graph of $y=\cos{(2x)}$ about the $x$-axis to obtain the graph of $y=-\cos{(2x)}$. Refer to the blue graph below.
