91Ó°ÊÓ

For a cosine function, the amplitude is the absolute value of the coefficient in front of the cosine term, which is 1 in this case. Therefore, the amplitude of the function is 1.

For a cosine function, the period is \(\frac{2\pi}{|B|}\), where \(B\) is the coefficient of the variable inside the cosine term (B = 1 in this case). In the given function, \(y = \cos(x+\pi)\), the value of \(B\) is 1, so the period is \(\frac{2\pi}{1}\), which simplifies to \(2\pi\).

To determine the horizontal shift, look at the value inside the cosine function. In our case, it is \(x+\pi\). Since a positive value inside the function will shift the graph to the left, the horizontal shift is \(\pi\) units to the left.

Start by drawing the cosine function \(y = \cos(x)\) from \(0\) to \(2\pi\) (one period). Next, shift the graph \(\pi\) units to the left to get the graph of the given function \(y = \cos(x+\pi)\). When you sketch this graph, make sure it has the correct amplitude (maximum value 1 and minimum value -1) and period (no more than \(2\pi\) wide). The graph of the function \(y = \cos(x+\pi)\) should look like a regular cosine curve that starts at the origin with the maximum value (1), goes down to its minimum value (-1) at \(\frac{\pi}{2}\), returns to the maximum value (1) at \(\pi\), and finally ends at \(2\pi\) with the maximum value again. The graph will be shifted \(\pi\) units to the left compared to the standard cosine graph.