Graph y=-4sin(x)

Problem

y=−4*sin(x)

Solution

1. Identify the parent function and its properties. The base function is y=sin(x) which has a period of 2*π an amplitude of 1 and starts at the origin (0,0) moving upward.

2. Determine the amplitude of the given function. The coefficient in front of the sine function is −4 The amplitude is the absolute value |−4|=4 meaning the graph will reach a maximum height of 4 and a minimum height of −4

3. Identify the reflection across the x-axis. Because the coefficient is negative (−4, the graph of sin(x) is reflected vertically. Instead of starting at (0,0) and moving up to the maximum, it starts at (0,0) and moves down to the minimum.

4. Determine the period and key points. The coefficient of x is 1 so the period remains 2*π We divide the period into four equal intervals of π/2 to find the key points: (0,0) (π/2,−4) (π,0) ((3*π)/2,4) and (2*π,0)

5. Sketch the curve by plotting these key points and connecting them with a smooth, periodic wave.

Final Answer

y=−4*sin(x)

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