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Chapter 6: Q. 26 (page 429)

In Problems 19鈥�26, apply the methods of this and the previous section to graph each function. Be sure to label key points and show at least two periods.

y=-csc(-12蟺虫+蟺4)

Short Answer

Expert verified

The graph of the function y=-csc(-12蟺虫+蟺4)is:

Step by step solution

01

Step 1. Given

The functiony=-csc(-12蟺虫+蟺4)

To graph the function with at least two cycles.

02

Step 2. Find the amplitude, period and phase shift.

Compare the given function y=-csc((蟺2)(-x+12))with y=Asin(蝇x-蠒)+B

No amplitude.

Period,2蟺蝇=4

Phase shift, 蠒蝇=12

03

Step 3. Determine x-coordinates

One cycle begins at x=蠒蝇(12)and ends at

x=蠒蝇+2蟺蝇=12+4=92

To find the five key points, divide the interval (12,92)into four sub intervals, each of length 4梅4=1

12+1=3232+1=5252+1=7272+1=92

The x-coordinates are 12,32,52,72,92

04

Step 4. Determine the key points

Use these values of xto determine the key points on the graph:

The key points include (32,1),(72,-1),(-52,1),(-12,-1),(-92,-1)

05

Step 5. Sketch the graph

Plot these five points and fill in the graph of the function.

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