graph the function f(x) = -cos(x).

Explanation:

Step1: Recall cosine - function properties

The standard cosine function $y = \cos(x)$ has a period of $2\pi$, an amplitude of 1, and passes through the points $(0,1),(\frac{\pi}{2},0),(\pi, - 1),(\frac{3\pi}{2},0),(2\pi,1)$ etc.

Step2: Analyze the transformation

The function $y=-\cos(x)$ is a reflection of the function $y = \cos(x)$ about the $x$-axis. When $x = 0$, $y=-\cos(0)=-1$; when $x=\frac{\pi}{2}$, $y =-\cos(\frac{\pi}{2}) = 0$; when $x=\pi$, $y=-\cos(\pi)=1$; when $x=\frac{3\pi}{2}$, $y=-\cos(\frac{3\pi}{2}) = 0$; when $x = 2\pi$, $y=-\cos(2\pi)=-1$.

Step3: Plot the points

Plot the points $(0, - 1),(\frac{\pi}{2},0),(\pi,1),(\frac{3\pi}{2},0),(2\pi,-1)$ and their counterparts in the negative - $x$ direction. Then connect these points with a smooth curve to form a cosine - like wave. The amplitude of $y =-\cos(x)$ is 1 and the period is $2\pi$.

Answer:

The graph of $y =-\cos(x)$ is a cosine - wave reflected about the $x$-axis with an amplitude of 1 and a period of $2\pi$.