Sketch the function $y=\(\cos\]\left\)(x\(\right\))-1$ on the graph below.

• A.
• B.
• C.
• D.

Answer: (B)

Verified step by step guidance

1. Start by understanding the function y = \(\cos\)(x) - 1. This is a transformation of the basic cosine function y = \(\cos\)(x).
2. The transformation involves a vertical shift downward by 1 unit. This means that every point on the graph of y = \(\cos\)(x) will be moved down by 1 unit.
3. Recall that the cosine function y = \(\cos\)(x) has a maximum value of 1 and a minimum value of -1. With the transformation y = \(\cos\)(x) - 1, the maximum value becomes 0 and the minimum value becomes -2.
4. The period of the cosine function is 2\(\pi\), meaning it repeats every 2\(\pi\) units along the x-axis. This property remains unchanged in the transformed function y = \(\cos\)(x) - 1.
5. Sketch the graph by plotting key points: at x = 0, y = \(\cos\)(0) - 1 = 0; at x = \(\pi\)/2, y = \(\cos\)(\(\pi\)/2) - 1 = -1; at x = \(\pi\), y = \(\cos\)(\(\pi\)) - 1 = -2; and continue this pattern to complete the graph over the interval shown.