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Help please easy question!!?

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Analyze the function f(x) = - 2 cot 3x. Include:
- Domain and range
- Period
asked Dec 27, 2012 in TRIGONOMETRY by skylar Apprentice

2 Answers

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Domain:


Range:



Integers is the set of integers »

Number lines:

Domain:

-Pi-2 Pi -----   3-Pi ---  30Pi -- 32 Pi ----  3Pi4 Pi ----  3

Range:

 

Plots:

Tooltip

Tooltip

 

 

Source : http://www.wolframalpha.com
 

 

answered Jan 17, 2013 by richardson Scholar
0 votes

Let the function is y = f (x ) = -2 cot (3x ).

Compare the equation y = -2 cot (3x ) with y = a cot(bx - c ) where b > 0.

a = -2, b = 3 and c = 0.

First draw the graph of y = -2 cot (3x ).

The two consecutive vertical asymptotes of the graph y = a cot(bx - c ) can be found by solving the equations bx - c = 0 and bx - c = π.

∴ 3x = 0 and 3x = π.

x = 0 and x = π/3.

Therefore the two  consecutive  vertical  asymptotes  occur  at x = 0 and x = π/3.

The interval [0, π/3] corresponds to one cycle of the graph. The cycle begins with 0 and ends with π/3 and find the three middle values.

Between these two asymptotes x = 0 and x = π/3, plot a few points, including the x - intercept, as shown in the table.

x

y = -2 cot (3x)

(x , y )

0

y = -2 cot (3*0) = -2 cot0 = undefined

(0 , ∞)

π/6

y = -2 cot (3* π/6) = -2 cot(π/2) = -2 (0) = 0

(π/6 , 0)

π/4

y = -2 cot (3* π/4) = -2 cot(135) = -2 (-1) = 2

(π/4 , 2)

π/10

y = -2 cot (3* π/10) = -2 cot(54) = -2(0.72654) = -1.3084

(π/10, -1.3084)

π/3

y = -2 cot (3* π/3) = -2 cot(π) = undefined

(π/3, -∞)

First plotting the asymptotes.

The midpoint between two consecutive vertical asymptotes is an x - intercept of the graph. The period of the function y = -2 cot (3x) is the distance between two consecutive vertical asymptotes.

After plotting the asymptotes and the x - intercept, plot a few additional points between the two asymptotes and sketch one cycle. Finally, sketch one or two additional cycles to the left and right.

graph the function y=2+3cot(x+pi/6)

The domain of cotangent function, y = -2cot (3x) is - ∞ < x < ∞, where x not equal to integer multiplies of π/3 or x ≠ nπ/3 and x ≠ 0.

Observe the graph, the domain is R - {0, ±n(π/3)| n ∈ N} and range is the set of all real numbers R or (-∞, ).

Period is π / 3.

answered Jun 16, 2014 by joly Scholar

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