Graph y=-6sin(pi/3x)+4

Problem

y=−6*sin(π/3*x)+4

Solution

1. Identify the amplitude. The amplitude A is the absolute value of the coefficient of the sine function.

|a|=|−6|=6

2. Determine the period. The period P is calculated using the formula P=(2*π)/b where b is the coefficient of x

P=(2*π)/π/3=6

3. Find the vertical shift. The constant term added to the function represents the midline of the graph.

D=4

4. Determine the range. The graph oscillates between the midline plus and minus the amplitude.

Maximum=4+6=10

Minimum=4−6=−2

5. Identify the phase shift and reflection. There is no horizontal phase shift since there is no constant added to x inside the sine function. However, the negative sign in front of the amplitude reflects the graph across the midline.

6. Calculate key points. Divide the period into four equal intervals of 1.5 units to find the xcoordinates for the intercepts, maximums, and minimums starting from x=0

(0,4)

(1.5,−2)

(3,4)

(4.5,10)

(6,4)

Final Answer

y=−6*sin(π/3*x)+4

The graph is a reflected sine wave with amplitude 6 period 6 midline y=4 and range [−2,10]

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