graph the function f(x) = sin(x - π).

Explanation:

Step1: Use trigonometric identity

We know that $\sin(A - B)=\sin A\cos B-\cos A\sin B$. For $f(x)=\sin(x - \pi)$, we have $\sin(x-\pi)=\sin x\cos\pi-\cos x\sin\pi$. Since $\cos\pi=- 1$ and $\sin\pi = 0$, then $\sin(x - \pi)=-\sin x$.

Step2: Identify key - points of $y =-\sin x$

The standard sine function $y = \sin x$ has key - points:

• When $x = 0$, $y=-\sin(0)=0$;
• When $x=\frac{\pi}{2}$, $y =-\sin(\frac{\pi}{2})=-1$;
• When $x=\pi$, $y=-\sin(\pi)=0$;
• When $x=\frac{3\pi}{2}$, $y=-\sin(\frac{3\pi}{2}) = 1$;
• When $x = 2\pi$, $y=-\sin(2\pi)=0$.

Step3: Plot the points and draw the graph

Plot the points $(0,0),(\frac{\pi}{2},-1),(\pi,0),(\frac{3\pi}{2},1),(2\pi,0)$ on the given coordinate grid. Then, connect these points with a smooth curve. The graph of $y = f(x)=\sin(x - \pi)$ has an amplitude of $1$ and a period of $2\pi$, and it is a reflection of the graph of $y = \sin x$ about the $x$ - axis.

Answer:

Plot the points $(0,0),(\frac{\pi}{2},-1),(\pi,0),(\frac{3\pi}{2},1),(2\pi,0)$ and connect them with a smooth curve to get the graph of $y=\sin(x - \pi)$.