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Chapter 6: Q. 25 (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=-sec(2蟺虫+蟺)

Short Answer

Expert verified

The graph of the function y=-sec(2蟺虫+蟺)is:

Step by step solution

01

Step 1. Given

The functiony=-sec(2蟺虫+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=-sec(2蟺虫-(-蟺))with y=Asin(蝇x-蠒)+B

No amplitude

Period,2蟺蝇=1

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+1=12

To find the five key points, divide the interval (-12,12)into four sub intervals, each of length 1梅4=14

-12+14=-14

-14+14=0

0+14=14

14+14=12

The x-coordinates are -12,-14,0,14,12

04

Step 4. Determine the key points

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

The key points include (-12,-1),(-32,-1),(0,1),(32,-1),(12,-1)

05

Step 5. Sketch the graph

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

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