Graph y=4cos(x)

Problem

y=4*cos(x)

Solution

1. Identify the parent function and its properties. The base function is y=cos(x) which has an amplitude of 1 and a period of 2*π

2. Determine the amplitude of the given function. The coefficient 4 in front of the cosine function indicates a vertical stretch, making the amplitude |4|=4

3. Determine the period of the function. Since the coefficient of x is 1 the period remains 2*π

4. Identify key points for one full cycle starting from x=0 The cosine function starts at its maximum value.

• At x=0 y=4*cos(0)=4

• At x=π/2 y=4*cos(π/2)=0

• At x=π y=4*cos(π)=−4

• At x=(3*π)/2 y=4*cos((3*π)/2)=0

• At x=2*π y=4*cos(2*π)=4

5. Sketch the graph by plotting these key points and connecting them with a smooth, wave-like curve that oscillates between y=4 and y=−4

Final Answer

y=4*cos(x)

The graph is a cosine wave with an amplitude of 4 a period of 2*π a maximum at (0,4) and a minimum at (π,−4)

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