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Chapter 6: Q. 75 (page 411)

Find an equation for the graph.

Short Answer

Expert verified

The equation of the given graph is y=-4sin3x.

Step by step solution

01

Step 1. Determine the sinusoidal function.

Consider the given graph,

The type of sinusoid can be determined immediately by inspecting its y-intercept if its at a maximum(highest point) and a minimum(lowest point) or neither.

As the minimum is at its y-intercept, then the graph is a cosine function and A<0. Then,

ymax=4ymin=-4

02

Step 2. Find the amplitude and period.

Consider the given question,

A=-12ymax-yminA=-124--4A=-124+4A=-12脳8A=-4

The period is 2蟺3. So,

2蟺蝇=2蟺3蝇=3

03

Step 3. Form the equation.

Vertical shift,

b=12ymax+yminb=124-4b=120b=0

Consider the form of the function,

y=Asin蝇x+b

Substitute the values,

y=-4sin3x+0y=-4sin3x

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