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Chapter 6: Q. 32 (page 410)

In Problems 31鈥�34, match the given function to one of the graphs (A)鈥� (D).

Short Answer

Expert verified

The graph of the given function is graph (C)

Step by step solution

01

Step 1. Given information   

The trigonometric function is:

y=-3sin2x

02

Step 2. To determine the amplitude and period of the sinusoidal function.    

By comparing given function -3sin2xwith standard sinusoidal function Asin蝇x

We get amplitudeA=-3

Time period is T=2蟺蝇T=2蟺2T=蟺

So the graph of the given function will have time period 蟺and amplitude 3

03

Step 3. To find passing points of the graph 

At y-axis

x=0

then y=-3sin2.0y=-3sinoy=-3.0y=0

Graph will pass through (0,0)

when x=蟺4

then y=-3sin2.蟺4y=-3sin蟺2y=-3.1y=-3

So the graph will pass through (0,0) and蟺4,-3

Now look at the given graphs from A-D, we can see that

graph (C) has amplitude -3 , time period 蟺and passing point (0,0) and 蟺4,-3

So the graph for given function is graph (C)

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