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Chapter 6: Q. 28 (page 409)

In Problems 21鈥�30, match the given function to one of the graphs (A)鈥� (J).

Short Answer

Expert verified

The graph of the given function is graph (G)

Step by step solution

01

Step 1. Given information 

The trigonometric function is: y=-2cos蟺2x

02

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

By comparing given function -2cos蟺2xwith standard cosine function: Acos蝇x

We get amplitudeA=-2

Time period is 2蟺蟺2=4

So the graph of the given function will have time period 4 and amplitude -2

03

Step 3. To find value of function at y-axis.  

At y-axis

x=0

theny=-2cos蟺2.0y=-2cos0y=-2.1y=-2

graph will pass through (0,-2)

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

graph (G) has amplitude 2 , time period 4 and passing point (0,-2)

So the graph for given function is graph (G)

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