Graph y=-7cos(x)

Problem

y=−7*cos(x)

Solution

1. Identify the parent function and its key characteristics. The parent function is y=cos(x) which has a period of 2*π an amplitude of 1 and starts at a maximum point (0,1)

2. Determine the amplitude of the given function. The coefficient in front of the cosine function is −7 The amplitude is the absolute value of this coefficient, which is |−7|=7

3. Identify the reflection across the x-axis. Because the coefficient is negative, the graph of y=cos(x) is reflected vertically. Instead of starting at a maximum, the graph starts at a minimum point (0,−7)

4. Determine the period and key points. The coefficient of x is 1 so the period remains 2*π Divide the period into four equal intervals of π/2 to find the critical points: (0,−7) (π/2,0) (π,7) ((3*π)/2,0) and (2*π,−7)

5. Sketch the graph by plotting these five key points over one period and connecting them with a smooth, wave-like curve, then extending the pattern in both directions.

Final Answer

y=−7*cos(x)

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