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Chapter 6: Q. 24 (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=-tan(3x+蟺2)

Short Answer

Expert verified

The graph of the function y=-tan(3x+蟺2)is:

Step by step solution

01

Step 1. Given

The functiony=-tan(3x+蟺2)

To graph the function with at least two cycles.

02

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

Compare the given function y=-tan(3(x-(-蟺6)))with y=Asin(蝇x-蠒)+B

No amplitude

Period, 2蟺蝇=蟺3

Phase shift, 蠒蝇=-蟺6

03

Step 3. Determine coordinates

One cycle begins at x=蠒蝇(-蟺6)and ends at

x=蠒蝇+2蟺蝇=-蟺6+蟺3=蟺6

To find the five key points, divide the interval (-蟺6,蟺6)into four sub intervals, each of length 蟺3梅4=蟺12

-蟺6+蟺12=-蟺12

-蟺12+蟺12=0

0+蟺12=蟺12

蟺12+蟺12=蟺6

The x-coordinates are -蟺6,-蟺12,0,蟺12,蟺6

04

Step 4. Determine the key points

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

The key points include (-蟺6,0),(-蟺12,-1),(蟺4,-1),(蟺12,1),(蟺6,0)

05

Step 5. Sketch the graph

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

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