Question

1. $y = 3cos x - 1$, $0leq xleq 2pi$

Explanation:

Step1: Find key points

For \(y = 3\cos x-1\), when \(x = 0\), \(y=3\cos(0)-1=3\times1 - 1=2\); when \(x=\frac{\pi}{2}\), \(y = 3\cos(\frac{\pi}{2})-1=3\times0 - 1=-1\); when \(x=\pi\), \(y=3\cos(\pi)-1=3\times(- 1)-1=-4\); when \(x=\frac{3\pi}{2}\), \(y = 3\cos(\frac{3\pi}{2})-1=3\times0 - 1=-1\); when \(x = 2\pi\), \(y=3\cos(2\pi)-1=3\times1 - 1=2\).

Step2: Plot the points

Plot the points \((0,2)\), \((\frac{\pi}{2},-1)\), \((\pi,-4)\), \((\frac{3\pi}{2},-1)\), \((2\pi,2)\) on the coordinate system.

Step3: Draw the graph

Connect these points with a smooth curve. Since the function \(y = 3\cos x-1\) is a cosine - type function, its graph is a cosine - like curve within the interval \(0\leq x\leq2\pi\).

Answer:

The graph of \(y = 3\cos x-1\) for \(0\leq x\leq2\pi\) is a cosine - type curve passing through the points \((0,2)\), \((\frac{\pi}{2},-1)\), \((\pi,-4)\), \((\frac{3\pi}{2},-1)\), \((2\pi,2)\) and is drawn by connecting these points with a smooth curve.