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Chapter 6: Q. 39 (page 419)

graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

y=2csc13x-1

Short Answer

Expert verified

The domain of the function is{x|x鈮�k3蟺,kisaninteger}

The range of the function is (-鈭�,-3]鈭�[1,鈭�)

The graph of the functiony=2csc13x-1is

Step by step solution

01

Step 1. Given data

The given function is

y=2csc13x-1

02

Step 2. Graph of the parent function 

Parent function of y=2csc13x-1is y=cscx

Plot the graph of y=cscx

03

Step 3. Vertical stretch 

Plot y=2cscxby vertical stretching the graph of y=cscxby a factor of 2

04

Step 4. Horizontal stretch  

Plot by Horizontal stretching y=2csc13xthe graph of y=2cscxby a factor of 13

05

Step 5. Vertical shift 

Plot y=2csc13x-1by vertical shifting the graph of y=2csc13xto downward by one unit

06

Step 6. Domain and range 

The graph of function state that the

The domain of the function is{x|x鈮�3k蟺}

The range of the function is(-鈭�,-3]鈭�[1,鈭�)

07

Step 7. Verification 

Plot the graph of y=2csc13x-1using a graphing utility

The graph matches so our graph is correct.

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