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Chapter 6: Q. 22 (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=12sec(3x-蟺)

Short Answer

Expert verified

The graph of the function y=12sec(3x-蟺)is:

Step by step solution

01

Step 1. Given

The functiony=12sec(3x-蟺)

To graph the function with at least two cycles.

02

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

Compare the given function y=12sec(3(x-蟺3))with y=Asin(蝇x-蠒)+B

No amplitude

Period, 2蟺蝇=2蟺3

Phase shift, 蠒蝇=蟺3

03

Step 3. Determine x-coordinates

One cycle begins at x=蠒蝇(蟺3)and ends at

x=蠒蝇+2蟺蝇=蟺3+2蟺3=蟺

To find the five key points, divide the interval (蟺3,蟺)into four sub intervals, each of length 2蟺3梅4=蟺6

蟺3+蟺6=蟺2

蟺2+蟺6=2蟺3

2蟺3+蟺6=5蟺6

5蟺6+蟺6=蟺

The x-coordinates are 蟺3,蟺2,2蟺3,5蟺6,蟺

04

Step 4. Determine the key points

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

The key points include (蟺3,12),(-蟺3,12),(2蟺3,-12),(-2蟺3,-12),(蟺,12)

05

Step 5. Sketch the graph

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

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